cons_quadratic.c

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/* * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * */
/*                                                                           */
/*                  This file is part of the program and library             */
/*         SCIP --- Solving Constraint Integer Programs                      */
/*                                                                           */
/*    Copyright (C) 2002-2014 Konrad-Zuse-Zentrum                            */
/*                            fuer Informationstechnik Berlin                */
/*                                                                           */
/*  SCIP is distributed under the terms of the ZIB Academic License.         */
/*                                                                           */
/*  You should have received a copy of the ZIB Academic License              */
/*  along with SCIP; see the file COPYING. If not email to scip@zib.de.      */
/*                                                                           */
/* * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * */

/**@file   cons_quadratic.c
 * @brief  constraint handler for quadratic constraints \f$\textrm{lhs} \leq \sum_{i,j=1}^n a_{i,j} x_ix_j + \sum_{i=1}^n b_i x_i \leq \textrm{rhs}\f$
 * @author Stefan Vigerske
 * 
 * @todo SCIP might fix linear variables on +/- infinity; remove them in presolve and take care later
 * @todo round constraint sides to integers if all coefficients and variables are (impl.) integer
 * @todo constraints in one variable should be replaced by linear or bounddisjunction constraint
 * @todo check if some quadratic terms appear in several constraints and try to simplify (e.g., nous1)
 * @todo skip separation in enfolp if for current LP (check LP id) was already separated
 * @todo watch unbounded variables to enable/disable propagation
 * @todo sort order in bilinvar1/bilinvar2 such that the var which is involved in more terms is in bilinvar1, and use this info propagate and AddLinearReform
 * @todo catch/drop events in consEnable/consDisable, do initsol/exitsol stuff also when a constraint is enabled/disabled during solve
 * @todo underestimate for multivariate concave quadratic terms as in cons_nonlinear
 */

/*---+----1----+----2----+----3----+----4----+----5----+----6----+----7----+----8----+----9----+----0----+----1----+----2*/


#include <assert.h>
#include <string.h> /* for strcmp */ 
#include <ctype.h>  /* for isspace */
#include <math.h>

#include "scip/cons_nonlinear.h"
#include "scip/cons_quadratic.h"
#include "scip/cons_linear.h"
#include "scip/cons_and.h"
#include "scip/cons_varbound.h"
#include "scip/intervalarith.h"
#include "scip/heur_subnlp.h"
#include "scip/heur_trysol.h"
#include "scip/debug.h"
#include "nlpi/nlpi.h"
#include "nlpi/nlpi_ipopt.h"

/* constraint handler properties */
#define CONSHDLR_NAME          "quadratic"
#define CONSHDLR_DESC          "quadratic constraints of the form lhs <= b' x + x' A x <= rhs"
#define CONSHDLR_SEPAPRIORITY        10 /**< priority of the constraint handler for separation */
#define CONSHDLR_ENFOPRIORITY       -50 /**< priority of the constraint handler for constraint enforcing */
#define CONSHDLR_CHECKPRIORITY -4000000 /**< priority of the constraint handler for checking feasibility */
#define CONSHDLR_SEPAFREQ             1 /**< frequency for separating cuts; zero means to separate only in the root node */
#define CONSHDLR_PROPFREQ             1 /**< frequency for propagating domains; zero means only preprocessing propagation */
#define CONSHDLR_EAGERFREQ          100 /**< frequency for using all instead of only the useful constraints in separation,
                                         *   propagation and enforcement, -1 for no eager evaluations, 0 for first only */
#define CONSHDLR_MAXPREROUNDS        -1 /**< maximal number of presolving rounds the constraint handler participates in (-1: no limit) */
#define CONSHDLR_DELAYSEPA        FALSE /**< should separation method be delayed, if other separators found cuts? */
#define CONSHDLR_DELAYPROP        FALSE /**< should propagation method be delayed, if other propagators found reductions? */
#define CONSHDLR_DELAYPRESOL      FALSE /**< should presolving method be delayed, if other presolvers found reductions? */
#define CONSHDLR_NEEDSCONS         TRUE /**< should the constraint handler be skipped, if no constraints are available? */

#define CONSHDLR_PROP_TIMING SCIP_PROPTIMING_BEFORELP

#define MAXDNOM                 10000LL /**< maximal denominator for simple rational fixed values */
#define NONLINCONSUPGD_PRIORITY   40000 /**< priority of upgrading nonlinear constraints */
#define INITLPMAXVARVAL          1000.0 /**< maximal absolute value of variable for still generating a linearization cut at that point in initlp */

/* Activating this define enables reformulation of bilinear terms x*y with implications from x to y into linear terms.
 * However, implications are not enforced by SCIP. Thus, if, e.g., the used implication was derived from this constraint and we then reformulate the constraint,
 * then the implication may not be enforced in a solution.
 * This issue need to be fixed before this feature can be enabled.
 */
/* #define CHECKIMPLINBILINEAR */

/* enable new propagation for bivariate quadratic terms */
#define PROPBILINNEW

/*
 * Data structures
 */

/** eventdata for variable bound change events in quadratic constraints */
struct SCIP_QuadVarEventData
{
   SCIP_CONSDATA*        consdata;           /**< the constraint data */
   int                   varidx;             /**< the index of the variable which bound change is caught, positive for linear variables, negative for quadratic variables */
   int                   filterpos;          /**< position of eventdata in SCIP's event filter */
};

/** Data of a quadratic constraint. */
struct SCIP_ConsData
{
   SCIP_Real             lhs;                /**< left hand side of constraint */
   SCIP_Real             rhs;                /**< right hand side of constraint */

   int                   nlinvars;           /**< number of linear variables */
   int                   linvarssize;        /**< length of linear variable arrays */
   SCIP_VAR**            linvars;            /**< linear variables */
   SCIP_Real*            lincoefs;           /**< coefficients of linear variables */
   SCIP_QUADVAREVENTDATA** lineventdata;       /**< eventdata for bound change of linear variable */

   int                   nquadvars;          /**< number of variables in quadratic terms */
   int                   quadvarssize;       /**< length of quadratic variable terms arrays */
   SCIP_QUADVARTERM*     quadvarterms;       /**< array with quadratic variable terms */

   int                   nbilinterms;        /**< number of bilinear terms */
   int                   bilintermssize;     /**< length of bilinear term arrays */
   SCIP_BILINTERM*       bilinterms;         /**< bilinear terms array */

   SCIP_NLROW*           nlrow;              /**< a nonlinear row representation of this constraint */

   unsigned int          linvarssorted:1;    /**< are the linear variables already sorted? */
   unsigned int          linvarsmerged:1;    /**< are equal linear variables already merged? */
   unsigned int          quadvarssorted:1;   /**< are the quadratic variables already sorted? */
   unsigned int          quadvarsmerged:1;   /**< are equal quadratic variables already merged? */
   unsigned int          bilinsorted:1;      /**< are the bilinear terms already sorted? */
   unsigned int          bilinmerged:1;      /**< are equal bilinear terms already merged? */

   unsigned int          isconvex:1;         /**< is quadratic function is convex ? */
   unsigned int          isconcave:1;        /**< is quadratic function is concave ? */
   unsigned int          iscurvchecked:1;    /**< is quadratic function checked on convexity or concavity ? */
   unsigned int          isremovedfixings:1; /**< did we removed fixed/aggr/multiaggr variables ? */
   unsigned int          ispropagated:1;     /**< was the constraint propagated with respect to the current bounds ? */
   unsigned int          ispresolved:1;      /**< did we checked for possibilities of upgrading or implicit integer variables ? */
   unsigned int          initialmerge:1;     /**< did we perform an initial merge and clean in presolving yet ? */
#ifdef CHECKIMPLINBILINEAR
   unsigned int          isimpladded:1;      /**< has there been an implication added for a binary variable in a bilinear term? */
#endif

   SCIP_Real             minlinactivity;     /**< sum of minimal activities of all linear terms with finite minimal activity */
   SCIP_Real             maxlinactivity;     /**< sum of maximal activities of all linear terms with finite maximal activity */
   int                   minlinactivityinf;  /**< number of linear terms with infinite minimal activity */
   int                   maxlinactivityinf;  /**< number of linear terms with infinity maximal activity */
   SCIP_INTERVAL         quadactivitybounds; /**< bounds on the activity of the quadratic term, if up to date, otherwise empty interval */
   SCIP_Real             activity;           /**< activity of quadratic function w.r.t. current solution */
   SCIP_Real             lhsviol;            /**< violation of lower bound by current solution (used temporarily inside constraint handler) */
   SCIP_Real             rhsviol;            /**< violation of lower bound by current solution (used temporarily inside constraint handler) */

   int                   linvar_maydecrease; /**< index of a variable in linvars that may be decreased without making any other constraint infeasible, or -1 if none */
   int                   linvar_mayincrease; /**< index of a variable in linvars that may be increased without making any other constraint infeasible, or -1 if none */

   SCIP_VAR**            sepaquadvars;       /**< variables corresponding to quadvarterms to use in separation, only available in solving stage */
   int*                  sepabilinvar2pos;   /**< position of second variable in bilinear terms to use in separation, only available in solving stage */
   SCIP_Real             lincoefsmin;        /**< minimal absolute value of coefficients in linear part, only available in solving stage */
   SCIP_Real             lincoefsmax;        /**< maximal absolute value of coefficients in linear part, only available in solving stage */

   SCIP_Real*            factorleft;         /**< coefficients of left factor if constraint function is factorable */
   SCIP_Real*            factorright;        /**< coefficients of right factor if constraint function is factorable */
};

/** quadratic constraint update method */
struct SCIP_QuadConsUpgrade
{
   SCIP_DECL_QUADCONSUPGD((*quadconsupgd));  /**< method to call for upgrading quadratic constraint */
   int                   priority;           /**< priority of upgrading method */
   SCIP_Bool             active;             /**< is upgrading enabled */
};
typedef struct SCIP_QuadConsUpgrade SCIP_QUADCONSUPGRADE; /**< quadratic constraint update method */

/** constraint handler data */
struct SCIP_ConshdlrData
{
   int                   replacebinaryprodlength; /**< length of linear term which when multiplied with a binary variable is replaced by an auxiliary variable and an equivalent linear formulation */
   int                   empathy4and;        /**< how much empathy we have for using the AND constraint handler: 0 avoid always; 1 use sometimes; 2 use as often as possible */
   SCIP_Bool             binreforminitial;   /**< whether to make constraints added due to replacing products with binary variables initial */
   SCIP_Real             binreformmaxcoef;   /**< factor on 1/feastol to limit coefficients and coef range in linear constraints created by binary reformulation */
   SCIP_Real             mincutefficacysepa; /**< minimal efficacy of a cut in order to add it to relaxation during separation */
   SCIP_Real             mincutefficacyenfofac; /**< minimal target efficacy of a cut in order to add it to relaxation during enforcement as factor of feasibility tolerance (may be ignored) */
   char                  scaling;            /**< scaling method of constraints in feasibility check */
   SCIP_Real             cutmaxrange;        /**< maximal range (maximal coef / minimal coef) of a cut in order to be added to LP */
   SCIP_Bool             linearizeheursol;   /**< whether linearizations of convex quadratic constraints should be added to cutpool when some heuristics finds a new solution */
   SCIP_Bool             checkcurvature;     /**< whether functions should be checked for convexity/concavity */
   SCIP_Bool             checkfactorable;    /**< whether functions should be checked to be factorable */
   SCIP_Bool             linfeasshift;       /**< whether to make solutions in check feasible if possible */
   SCIP_Bool             disaggregate;       /**< whether to disaggregate quadratic constraints */
   int                   maxproprounds;      /**< limit on number of propagation rounds for a single constraint within one round of SCIP propagation during solve */
   int                   maxproproundspresolve; /**< limit on number of propagation rounds for a single constraint within one presolving round */
   SCIP_Real             sepanlpmincont;     /**< minimal required fraction of continuous variables in problem to use solution of NLP relaxation in root for separation */
   SCIP_Bool             enfocutsremovable;  /**< are cuts added during enforcement removable from the LP in the same node? */
   int                   enfolplimit;        /**< maximum number of enforcement round before declaring the LP relaxation
                                              * infeasible (-1: no limit); WARNING: if this parameter is not set to -1,
                                              * SCIP might declare sub-optimal solutions optimal or feasible instances
                                              * infeasible; thus, the result returned by SCIP might be incorrect!
                                              */
   SCIP_HEUR*            subnlpheur;         /**< a pointer to the subnlp heuristic, if available */
   SCIP_HEUR*            trysolheur;         /**< a pointer to the trysol heuristic, if available */
   SCIP_EVENTHDLR*       eventhdlr;          /**< our handler for variable bound change events */
   int                   newsoleventfilterpos; /**< filter position of new solution event handler, if caught */
   SCIP_Bool             sepanlp;            /**< where linearization of the NLP relaxation solution added? */
   SCIP_NODE*            lastenfolpnode;     /**< the node for which enforcement was called the last time (and some constraint was violated) */
   int                   nenfolprounds;      /**< counter on number of enforcement rounds for the current node */
   SCIP_QUADCONSUPGRADE** quadconsupgrades;  /**< quadratic constraint upgrade methods for specializing quadratic constraints */
   int                   quadconsupgradessize; /**< size of quadconsupgrade array */
   int                   nquadconsupgrades;  /**< number of quadratic constraint upgrade methods */
};


/*
 * local methods for managing quadratic constraint update methods
 */


/** checks whether a quadratic constraint upgrade method has already be registered */
static
SCIP_Bool conshdlrdataHasUpgrade(
   SCIP*                 scip,               /**< SCIP data structure */
   SCIP_CONSHDLRDATA*    conshdlrdata,       /**< constraint handler data */
   SCIP_DECL_QUADCONSUPGD((*quadconsupgd)),  /**< method to call for upgrading quadratic constraint */
   const char*           conshdlrname        /**< name of the constraint handler */
   )
{
   int i;

   assert(scip != NULL);
   assert(conshdlrdata != NULL);
   assert(quadconsupgd != NULL);
   assert(conshdlrname != NULL);

   for( i = conshdlrdata->nquadconsupgrades - 1; i >= 0; --i )
   {
      if( conshdlrdata->quadconsupgrades[i]->quadconsupgd == quadconsupgd )
      {
         SCIPwarningMessage(scip, "Try to add already known upgrade message for constraint handler <%s>.\n", conshdlrname);
         return TRUE;
      }
   }

   return FALSE;
}

/*
 * Local methods
 */

/** translate from one value of infinity to another
 * 
 *  if val is >= infty1, then give infty2, else give val
 */
#define infty2infty(infty1, infty2, val) ((val) >= (infty1) ? (infty2) : (val))

/* catches variable bound change events on a linear variable in a quadratic constraint */
static
SCIP_RETCODE catchLinearVarEvents(
   SCIP*                 scip,               /**< SCIP data structure */
   SCIP_EVENTHDLR*       eventhdlr,          /**< event handler */
   SCIP_CONS*            cons,               /**< constraint for which to catch bound change events */
   int                   linvarpos           /**< position of variable in linear variables array */
   )
{
   SCIP_CONSDATA*  consdata;
   SCIP_QUADVAREVENTDATA* eventdata;
   SCIP_EVENTTYPE  eventtype;

   assert(scip != NULL);
   assert(eventhdlr != NULL);
   assert(cons != NULL);

   consdata = SCIPconsGetData(cons);
   assert(consdata != NULL);

   assert(linvarpos >= 0);
   assert(linvarpos < consdata->nlinvars);
   assert(consdata->lineventdata != NULL);

   SCIP_CALL( SCIPallocBlockMemory(scip, &eventdata) );

   eventdata->consdata = consdata;
   eventdata->varidx = linvarpos;

   eventtype = SCIP_EVENTTYPE_VARFIXED;
   if( !SCIPisInfinity(scip, consdata->rhs) )
   {
      /* if right hand side is finite, then a tightening in the lower bound of coef*linvar is of interest
       * since we also want to keep activities in consdata up-to-date, we also need to know when the corresponding bound is relaxed */
      if( consdata->lincoefs[linvarpos] > 0.0 )
         eventtype |= SCIP_EVENTTYPE_LBCHANGED;
      else
         eventtype |= SCIP_EVENTTYPE_UBCHANGED;
   }
   if( !SCIPisInfinity(scip, -consdata->lhs) )
   {
      /* if left hand side is finite, then a tightening in the upper bound of coef*linvar is of interest
       * since we also want to keep activities in consdata up-to-date, we also need to know when the corresponding bound is relaxed */
      if( consdata->lincoefs[linvarpos] > 0.0 )
         eventtype |= SCIP_EVENTTYPE_UBCHANGED;
      else
         eventtype |= SCIP_EVENTTYPE_LBCHANGED;
   }

   SCIP_CALL( SCIPcatchVarEvent(scip, consdata->linvars[linvarpos], eventtype, eventhdlr, (SCIP_EVENTDATA*)eventdata, &eventdata->filterpos) );

   consdata->lineventdata[linvarpos] = eventdata;

   /* invalidate activity information
    * NOTE: It could happen that a constraint gets temporary deactivated and some variable bounds change. In this case
    *       we do not recognize those bound changes with the variable events and thus we have to recompute the activities.
    */
   consdata->minlinactivity = SCIP_INVALID;
   consdata->maxlinactivity = SCIP_INVALID;
   consdata->minlinactivityinf = -1;
   consdata->maxlinactivityinf = -1;

   return SCIP_OKAY;
}

/* drops variable bound change events on a linear variable in a quadratic constraint */
static
SCIP_RETCODE dropLinearVarEvents(
   SCIP*                 scip,               /**< SCIP data structure */
   SCIP_EVENTHDLR*       eventhdlr,          /**< event handler */
   SCIP_CONS*            cons,               /**< constraint for which to catch bound change events */
   int                   linvarpos           /**< position of variable in linear variables array */
   )
{
   SCIP_CONSDATA* consdata;
   SCIP_EVENTTYPE  eventtype;

   assert(scip != NULL);
   assert(eventhdlr != NULL);
   assert(cons != NULL);

   consdata = SCIPconsGetData(cons);
   assert(consdata != NULL);

   assert(linvarpos >= 0);
   assert(linvarpos < consdata->nlinvars);
   assert(consdata->lineventdata != NULL);
   assert(consdata->lineventdata[linvarpos] != NULL);
   assert(consdata->lineventdata[linvarpos]->consdata == consdata);
   assert(consdata->lineventdata[linvarpos]->varidx == linvarpos);
   assert(consdata->lineventdata[linvarpos]->filterpos >= 0);

   eventtype = SCIP_EVENTTYPE_VARFIXED;
   if( !SCIPisInfinity(scip, consdata->rhs) )
   {
      /* if right hand side is finite, then a tightening in the lower bound of coef*linvar is of interest
       * since we also want to keep activities in consdata up-to-date, we also need to know when the corresponding bound is relaxed */
      if( consdata->lincoefs[linvarpos] > 0.0 )
         eventtype |= SCIP_EVENTTYPE_LBCHANGED;
      else
         eventtype |= SCIP_EVENTTYPE_UBCHANGED;
   }
   if( !SCIPisInfinity(scip, -consdata->lhs) )
   {
      /* if left hand side is finite, then a tightening in the upper bound of coef*linvar is of interest
       * since we also want to keep activities in consdata up-to-date, we also need to know when the corresponding bound is relaxed */
      if( consdata->lincoefs[linvarpos] > 0.0 )
         eventtype |= SCIP_EVENTTYPE_UBCHANGED;
      else
         eventtype |= SCIP_EVENTTYPE_LBCHANGED;
   }

   SCIP_CALL( SCIPdropVarEvent(scip, consdata->linvars[linvarpos], eventtype, eventhdlr, (SCIP_EVENTDATA*)consdata->lineventdata[linvarpos], consdata->lineventdata[linvarpos]->filterpos) );

   SCIPfreeBlockMemory(scip, &consdata->lineventdata[linvarpos]);  /*lint !e866 */

   return SCIP_OKAY;
}

/* catches variable bound change events on a quadratic variable in a quadratic constraint */
static
SCIP_RETCODE catchQuadVarEvents(
   SCIP*                 scip,               /**< SCIP data structure */
   SCIP_EVENTHDLR*       eventhdlr,          /**< event handler */
   SCIP_CONS*            cons,               /**< constraint for which to catch bound change events */
   int                   quadvarpos          /**< position of variable in quadratic variables array */
   )
{
   SCIP_CONSDATA* consdata;
   SCIP_QUADVAREVENTDATA* eventdata;
   SCIP_EVENTTYPE eventtype;

   assert(scip != NULL);
   assert(eventhdlr != NULL);
   assert(cons != NULL);

   consdata = SCIPconsGetData(cons);
   assert(consdata != NULL);

   assert(quadvarpos >= 0);
   assert(quadvarpos < consdata->nquadvars);
   assert(consdata->quadvarterms[quadvarpos].eventdata == NULL);

   SCIP_CALL( SCIPallocBlockMemory(scip, &eventdata) );

   eventtype = SCIP_EVENTTYPE_BOUNDCHANGED | SCIP_EVENTTYPE_VARFIXED;
#ifdef CHECKIMPLINBILINEAR
   eventtype |= SCIP_EVENTTYPE_IMPLADDED;
#endif
   eventdata->consdata = consdata;
   eventdata->varidx   = -quadvarpos-1;
   SCIP_CALL( SCIPcatchVarEvent(scip, consdata->quadvarterms[quadvarpos].var, eventtype, eventhdlr, (SCIP_EVENTDATA*)eventdata, &eventdata->filterpos) );

   consdata->quadvarterms[quadvarpos].eventdata = eventdata;

   /* invalidate activity information
    * NOTE: It could happen that a constraint gets temporary deactivated and some variable bounds change. In this case
    *       we do not recognize those bound changes with the variable events and thus we have to recompute the activities.
    */
   SCIPintervalSetEmpty(&consdata->quadactivitybounds);

   return SCIP_OKAY;
}

/* catches variable bound change events on a quadratic variable in a quadratic constraint */
static
SCIP_RETCODE dropQuadVarEvents(
   SCIP*                 scip,               /**< SCIP data structure */
   SCIP_EVENTHDLR*       eventhdlr,          /**< event handler */
   SCIP_CONS*            cons,               /**< constraint for which to catch bound change events */
   int                   quadvarpos          /**< position of variable in quadratic variables array */
   )
{
   SCIP_CONSDATA* consdata;
   SCIP_EVENTTYPE eventtype;

   assert(scip != NULL);
   assert(eventhdlr != NULL);
   assert(cons != NULL);

   consdata = SCIPconsGetData(cons);
   assert(consdata != NULL);

   assert(quadvarpos >= 0);
   assert(quadvarpos < consdata->nquadvars);
   assert(consdata->quadvarterms[quadvarpos].eventdata != NULL);
   assert(consdata->quadvarterms[quadvarpos].eventdata->consdata == consdata);
   assert(consdata->quadvarterms[quadvarpos].eventdata->varidx == -quadvarpos-1);
   assert(consdata->quadvarterms[quadvarpos].eventdata->filterpos >= 0);

   eventtype = SCIP_EVENTTYPE_BOUNDCHANGED | SCIP_EVENTTYPE_VARFIXED;
#ifdef CHECKIMPLINBILINEAR
   eventtype |= SCIP_EVENTTYPE_IMPLADDED;
#endif

   SCIP_CALL( SCIPdropVarEvent(scip, consdata->quadvarterms[quadvarpos].var, eventtype, eventhdlr, (SCIP_EVENTDATA*)consdata->quadvarterms[quadvarpos].eventdata, consdata->quadvarterms[quadvarpos].eventdata->filterpos) );

   SCIPfreeBlockMemory(scip, &consdata->quadvarterms[quadvarpos].eventdata);

   return SCIP_OKAY;
}

/** catch variable events */
static
SCIP_RETCODE catchVarEvents(
   SCIP*                 scip,               /**< SCIP data structure */
   SCIP_EVENTHDLR*       eventhdlr,          /**< event handler */
   SCIP_CONS*            cons                /**< constraint for which to catch bound change events */      
   )
{
   SCIP_CONSDATA* consdata;
   int i;

   assert(scip != NULL);
   assert(cons != NULL);
   assert(eventhdlr != NULL);

   consdata = SCIPconsGetData(cons);
   assert(consdata != NULL);
   assert(consdata->lineventdata == NULL);

   /* we will update isremovedfixings, so reset it to TRUE first */
   consdata->isremovedfixings = TRUE;

   SCIP_CALL( SCIPallocBlockMemoryArray(scip, &consdata->lineventdata, consdata->linvarssize) );
   for( i = 0; i < consdata->nlinvars; ++i )
   {
      SCIP_CALL( catchLinearVarEvents(scip, eventhdlr, cons, i) );

      consdata->isremovedfixings = consdata->isremovedfixings && SCIPvarIsActive(consdata->linvars[i]);
   }

   for( i = 0; i < consdata->nquadvars; ++i )
   {
      assert(consdata->quadvarterms[i].eventdata == NULL);

      SCIP_CALL( catchQuadVarEvents(scip, eventhdlr, cons, i) );

      consdata->isremovedfixings = consdata->isremovedfixings && SCIPvarIsActive(consdata->quadvarterms[i].var);
   }

   consdata->ispropagated = FALSE;

   return SCIP_OKAY;
}

/** drop variable events */
static
SCIP_RETCODE dropVarEvents(
   SCIP*                 scip,               /**< SCIP data structure */
   SCIP_EVENTHDLR*       eventhdlr,          /**< event handler */
   SCIP_CONS*            cons                /**< constraint for which to drop bound change events */
   )
{
   SCIP_CONSDATA* consdata;
   int i;

   assert(scip != NULL);
   assert(eventhdlr != NULL);
   assert(cons != NULL);

   consdata = SCIPconsGetData(cons);
   assert(consdata != NULL);

   if( consdata->lineventdata != NULL )
   {
      for( i = 0; i < consdata->nlinvars; ++i )
      {
         if( consdata->lineventdata[i] != NULL )
         {
            SCIP_CALL( dropLinearVarEvents(scip, eventhdlr, cons, i) );
         }
      }
      SCIPfreeBlockMemoryArray(scip, &consdata->lineventdata, consdata->linvarssize);
   }

   for( i = 0; i < consdata->nquadvars; ++i )
   {
      if( consdata->quadvarterms[i].eventdata != NULL )
      {
         SCIP_CALL( dropQuadVarEvents(scip, eventhdlr, cons, i) );
      }
   }

   return SCIP_OKAY;
}

/** locks a linear variable in a constraint */
static
SCIP_RETCODE lockLinearVariable(
   SCIP*                 scip,               /**< SCIP data structure */
   SCIP_CONS*            cons,               /**< constraint where to lock a variable */
   SCIP_VAR*             var,                /**< variable to lock */
   SCIP_Real             coef                /**< coefficient of variable in constraint */
   )
{
   SCIP_CONSDATA* consdata;

   assert(scip != NULL);
   assert(cons != NULL);
   assert(var != NULL);
   assert(coef != 0.0);

   consdata = SCIPconsGetData(cons);
   assert(consdata != NULL);

   if( coef > 0.0 )
   {
      SCIP_CALL( SCIPlockVarCons(scip, var, cons, !SCIPisInfinity(scip, -consdata->lhs), !SCIPisInfinity(scip,  consdata->rhs)) );
   }
   else
   {
      SCIP_CALL( SCIPlockVarCons(scip, var, cons, !SCIPisInfinity(scip,  consdata->rhs), !SCIPisInfinity(scip, -consdata->lhs)) );
   }

   return SCIP_OKAY;
}

/** unlocks a linear variable in a constraint */
static
SCIP_RETCODE unlockLinearVariable(
   SCIP*                 scip,               /**< SCIP data structure */
   SCIP_CONS*            cons,               /**< constraint where to unlock a variable */
   SCIP_VAR*             var,                /**< variable to unlock */
   SCIP_Real             coef                /**< coefficient of variable in constraint */
   )
{
   SCIP_CONSDATA* consdata;

   assert(scip != NULL);
   assert(cons != NULL);
   assert(var != NULL);
   assert(coef != 0.0);

   consdata = SCIPconsGetData(cons);
   assert(consdata != NULL);

   if( coef > 0.0 )
   {
      SCIP_CALL( SCIPunlockVarCons(scip, var, cons, !SCIPisInfinity(scip, -consdata->lhs), !SCIPisInfinity(scip,  consdata->rhs)) );
   }
   else
   {
      SCIP_CALL( SCIPunlockVarCons(scip, var, cons, !SCIPisInfinity(scip,  consdata->rhs), !SCIPisInfinity(scip, -consdata->lhs)) );
   }

   return SCIP_OKAY;
}

/** locks a quadratic variable in a constraint */
static
SCIP_RETCODE lockQuadraticVariable(
   SCIP*                 scip,               /**< SCIP data structure */
   SCIP_CONS*            cons,               /**< constraint where to lock a variable */
   SCIP_VAR*             var                 /**< variable to lock */
   )
{
   SCIP_CALL( SCIPlockVarCons(scip, var, cons, TRUE, TRUE) );

   return SCIP_OKAY;
}

/** unlocks a quadratic variable in a constraint */
static
SCIP_RETCODE unlockQuadraticVariable(
   SCIP*                 scip,               /**< SCIP data structure */
   SCIP_CONS*            cons,               /**< constraint where to unlock a variable */
   SCIP_VAR*             var                 /**< variable to unlock */
   )
{
   SCIP_CALL( SCIPunlockVarCons(scip, var, cons, TRUE, TRUE) );

   return SCIP_OKAY;
}

/** computes the minimal and maximal activity for the linear part in a constraint data
 *  only sums up terms that contribute finite values
 *  gives the number of terms that contribute infinite values
 *  only computes those activities where the corresponding side of the constraint is finite
 */
static
void consdataUpdateLinearActivity(
   SCIP*                 scip,               /**< SCIP data structure */
   SCIP_CONSDATA*        consdata,           /**< constraint data */
   SCIP_Real             intervalinfty       /**< infinity value used in interval operations */
   )
{  /*lint --e{666}*/
   SCIP_ROUNDMODE prevroundmode;
   int       i;
   SCIP_Real bnd;

   assert(scip != NULL);
   assert(consdata != NULL);

   /* if variable bounds are not strictly consistent, then the activity update methods may yield inconsistent activities
    * in this case, we also recompute the activities
    */
   if( consdata->minlinactivity != SCIP_INVALID && consdata->maxlinactivity != SCIP_INVALID &&  /*lint !e777 */
      (consdata->minlinactivityinf > 0 || consdata->maxlinactivityinf > 0 || consdata->minlinactivity <= consdata->maxlinactivity) )
   {
      /* activities should be up-to-date */
      assert(consdata->minlinactivityinf >= 0);
      assert(consdata->maxlinactivityinf >= 0);
      return;
   }

   consdata->minlinactivityinf = 0;
   consdata->maxlinactivityinf = 0;

   /* if lhs is -infinite, then we do not compute a maximal activity, so we set it to  infinity
    * if rhs is  infinite, then we do not compute a minimal activity, so we set it to -infinity
    */
   consdata->minlinactivity = SCIPisInfinity(scip,  consdata->rhs) ? -intervalinfty : 0.0;
   consdata->maxlinactivity = SCIPisInfinity(scip, -consdata->lhs) ?  intervalinfty : 0.0;

   if( consdata->nlinvars == 0 )
      return;

   /* if the activities computed here should be still up-to-date after bound changes,
    * variable events need to be caught */
   assert(consdata->lineventdata != NULL);

   prevroundmode = SCIPintervalGetRoundingMode();

   if( !SCIPisInfinity(scip,  consdata->rhs) )
   {
      /* compute minimal activity only if there is a finite right hand side */
      SCIPintervalSetRoundingModeDownwards();

      for( i = 0; i < consdata->nlinvars; ++i )
      {
         assert(consdata->lineventdata[i] != NULL);
         if( consdata->lincoefs[i] >= 0.0 )
         {
            bnd = MIN(SCIPvarGetLbLocal(consdata->linvars[i]), SCIPvarGetUbLocal(consdata->linvars[i]));
            if( SCIPisInfinity(scip, -bnd) )
            {
               ++consdata->minlinactivityinf;
               continue;
            }
            assert(!SCIPisInfinity(scip, bnd)); /* do not like variables that are fixed at +infinity */
         }
         else
         {
            bnd = MAX(SCIPvarGetLbLocal(consdata->linvars[i]), SCIPvarGetUbLocal(consdata->linvars[i]));
            if( SCIPisInfinity(scip,  bnd) )
            {
               ++consdata->minlinactivityinf;
               continue;
            }
            assert(!SCIPisInfinity(scip, -bnd)); /* do not like variables that are fixed at -infinity */
         }
         consdata->minlinactivity += consdata->lincoefs[i] * bnd;
      }
   }

   if( !SCIPisInfinity(scip, -consdata->lhs) )
   {
      /* compute maximal activity only if there is a finite left hand side */
      SCIPintervalSetRoundingModeUpwards();

      for( i = 0; i < consdata->nlinvars; ++i )
      {
         assert(consdata->lineventdata[i] != NULL);
         if( consdata->lincoefs[i] >= 0.0 )
         {
            bnd = MAX(SCIPvarGetLbLocal(consdata->linvars[i]), SCIPvarGetUbLocal(consdata->linvars[i]));
            if( SCIPisInfinity(scip,  bnd) )
            {
               ++consdata->maxlinactivityinf;
               continue;
            }
            assert(!SCIPisInfinity(scip, -bnd)); /* do not like variables that are fixed at -infinity */
         }
         else
         {
            bnd = MIN(SCIPvarGetLbLocal(consdata->linvars[i]), SCIPvarGetUbLocal(consdata->linvars[i]));
            if( SCIPisInfinity(scip, -bnd) )
            {
               ++consdata->maxlinactivityinf;
               continue;
            }
            assert(!SCIPisInfinity(scip, bnd)); /* do not like variables that are fixed at +infinity */
         }
         consdata->maxlinactivity += consdata->lincoefs[i] * bnd;
      }
   }

   SCIPintervalSetRoundingMode(prevroundmode);

   assert(consdata->minlinactivityinf > 0 || consdata->maxlinactivityinf > 0 || consdata->minlinactivity <= consdata->maxlinactivity);
}

/** update the linear activities after a change in the lower bound of a variable */
static
void consdataUpdateLinearActivityLbChange(
   SCIP*                 scip,               /**< SCIP data structure */
   SCIP_CONSDATA*        consdata,           /**< constraint data */
   SCIP_Real             coef,               /**< coefficient of variable in constraint */
   SCIP_Real             oldbnd,             /**< previous lower bound of variable */
   SCIP_Real             newbnd              /**< new lower bound of variable */
   )
{
   SCIP_ROUNDMODE prevroundmode;

   assert(scip != NULL);
   assert(consdata != NULL);
   /* we can't deal with lower bounds at infinity */
   assert(!SCIPisInfinity(scip, oldbnd));
   assert(!SCIPisInfinity(scip, newbnd));

   /* @todo since we check the linear activity for consistency later anyway, we may skip changing the rounding mode here */

   /* assume lhs <= a*x + y <= rhs, then the following bound changes can be deduced:
    * a > 0:  y <= rhs - a*lb(x),  y >= lhs - a*ub(x)
    * a < 0:  y <= rhs - a*ub(x),  y >= lhs - a*lb(x)
    */

   if( coef > 0.0 )
   {
      /* we should only be called if rhs is finite */
      assert(!SCIPisInfinity(scip, consdata->rhs));

      /* we have no min activities computed so far, so cannot update */
      if( consdata->minlinactivity == SCIP_INVALID )  /*lint !e777 */
         return;

      assert(!SCIPisInfinity(scip, -consdata->minlinactivity));

      prevroundmode = SCIPintervalGetRoundingMode();
      SCIPintervalSetRoundingModeDownwards();

      /* update min activity */
      if( SCIPisInfinity(scip, -oldbnd) )
      {
         --consdata->minlinactivityinf;
         assert(consdata->minlinactivityinf >= 0);
      }
      else
      {
         SCIP_Real minuscoef;
         minuscoef = -coef;
         consdata->minlinactivity += minuscoef * oldbnd;
      }

      if( SCIPisInfinity(scip, -newbnd) )
      {
         ++consdata->minlinactivityinf;
      }
      else
      {
         consdata->minlinactivity += coef * newbnd;
      }

      SCIPintervalSetRoundingMode(prevroundmode);
   }
   else
   {
      /* we should only be called if lhs is finite */
      assert(!SCIPisInfinity(scip, -consdata->lhs));

      /* we have no max activities computed so far, so cannot update */
      if( consdata->maxlinactivity == SCIP_INVALID )  /*lint !e777 */
         return;

      assert(!SCIPisInfinity(scip, consdata->maxlinactivity));

      prevroundmode = SCIPintervalGetRoundingMode();
      SCIPintervalSetRoundingModeUpwards();

      /* update max activity */
      if( SCIPisInfinity(scip, -oldbnd) )
      {
         --consdata->maxlinactivityinf;
         assert(consdata->maxlinactivityinf >= 0);
      }
      else
      {
         SCIP_Real minuscoef;
         minuscoef = -coef;
         consdata->maxlinactivity += minuscoef * oldbnd;
      }

      if( SCIPisInfinity(scip, -newbnd) )
      {
         ++consdata->maxlinactivityinf;
      }
      else
      {
         consdata->maxlinactivity += coef * newbnd;
      }

      SCIPintervalSetRoundingMode(prevroundmode);
   }
}

/** update the linear activities after a change in the upper bound of a variable */
static
void consdataUpdateLinearActivityUbChange(
   SCIP*                 scip,               /**< SCIP data structure */
   SCIP_CONSDATA*        consdata,           /**< constraint data */
   SCIP_Real             coef,               /**< coefficient of variable in constraint */
   SCIP_Real             oldbnd,             /**< previous lower bound of variable */
   SCIP_Real             newbnd              /**< new lower bound of variable */
   )
{
   SCIP_ROUNDMODE prevroundmode;

   assert(scip != NULL);
   assert(consdata != NULL);
   /* we can't deal with upper bounds at -infinity */
   assert(!SCIPisInfinity(scip, -oldbnd));
   assert(!SCIPisInfinity(scip, -newbnd));

   /* @todo since we check the linear activity for consistency later anyway, we may skip changing the rounding mode here */

   /* assume lhs <= a*x + y <= rhs, then the following bound changes can be deduced:
    * a > 0:  y <= rhs - a*lb(x),  y >= lhs - a*ub(x)
    * a < 0:  y <= rhs - a*ub(x),  y >= lhs - a*lb(x)
    */

   if( coef > 0.0 )
   {
      /* we should only be called if lhs is finite */
      assert(!SCIPisInfinity(scip, -consdata->lhs));

      /* we have no max activities computed so far, so cannot update */
      if( consdata->maxlinactivity == SCIP_INVALID )  /*lint !e777 */
         return;

      assert(!SCIPisInfinity(scip, consdata->maxlinactivity));

      prevroundmode = SCIPintervalGetRoundingMode();
      SCIPintervalSetRoundingModeUpwards();

      /* update max activity */
      if( SCIPisInfinity(scip, oldbnd) )
      {
         --consdata->maxlinactivityinf;
         assert(consdata->maxlinactivityinf >= 0);
      }
      else
      {
         SCIP_Real minuscoef;
         minuscoef = -coef;
         consdata->maxlinactivity += minuscoef * oldbnd;
      }

      if( SCIPisInfinity(scip, newbnd) )
      {
         ++consdata->maxlinactivityinf;
      }
      else
      {
         consdata->maxlinactivity += coef * newbnd;
      }

      SCIPintervalSetRoundingMode(prevroundmode);
   }
   else
   {
      /* we should only be called if rhs is finite */
      assert(!SCIPisInfinity(scip, consdata->rhs));

      /* we have no min activities computed so far, so cannot update */
      if( consdata->minlinactivity == SCIP_INVALID )  /*lint !e777 */
         return;

      assert(!SCIPisInfinity(scip, -consdata->minlinactivity));

      prevroundmode = SCIPintervalGetRoundingMode();
      SCIPintervalSetRoundingModeDownwards();

      /* update min activity */
      if( SCIPisInfinity(scip, oldbnd) )
      {
         --consdata->minlinactivityinf;
         assert(consdata->minlinactivityinf >= 0);
      }
      else
      {
         SCIP_Real minuscoef;
         minuscoef = -coef;
         consdata->minlinactivity += minuscoef * oldbnd;
      }

      if( SCIPisInfinity(scip, newbnd) )
      {
         ++consdata->minlinactivityinf;
      }
      else
      {
         consdata->minlinactivity += coef * newbnd;
      }

      SCIPintervalSetRoundingMode(prevroundmode);
   }
}

/** processes variable fixing or bound change event */
static
SCIP_DECL_EVENTEXEC(processVarEvent)
{
   SCIP_CONSDATA* consdata;
   SCIP_EVENTTYPE eventtype;
   int varidx;

   assert(scip != NULL);
   assert(event != NULL);
   assert(eventdata != NULL);
   assert(eventhdlr != NULL);

   consdata = ((SCIP_QUADVAREVENTDATA*)eventdata)->consdata;
   assert(consdata != NULL);

   varidx = ((SCIP_QUADVAREVENTDATA*)eventdata)->varidx;
   assert(varidx <  0 ||  varidx   < consdata->nlinvars);
   assert(varidx >= 0 || -varidx-1 < consdata->nquadvars);

   eventtype = SCIPeventGetType(event);

   if( eventtype & SCIP_EVENTTYPE_BOUNDCHANGED )
   {
      if( varidx < 0 )
      {
         /* mark activity bounds for quad term as not up to date anymore */
         SCIPintervalSetEmpty(&consdata->quadactivitybounds);
      }
      else
      {
         /* update activity bounds for linear terms */
         if( eventtype & SCIP_EVENTTYPE_LBCHANGED )
            consdataUpdateLinearActivityLbChange(scip, consdata, consdata->lincoefs[varidx], SCIPeventGetOldbound(event), SCIPeventGetNewbound(event));
         else
            consdataUpdateLinearActivityUbChange(scip, consdata, consdata->lincoefs[varidx], SCIPeventGetOldbound(event), SCIPeventGetNewbound(event));
      }

      if( eventtype & SCIP_EVENTTYPE_BOUNDTIGHTENED )
         consdata->ispropagated = FALSE;
   }

   if( eventtype & SCIP_EVENTTYPE_VARFIXED )
   {
      consdata->isremovedfixings = FALSE;
   }

#ifdef CHECKIMPLINBILINEAR
   if( eventtype & SCIP_EVENTTYPE_IMPLADDED )
   {
      assert(varidx < 0); /* we catch impladded events only for quadratic variables */
      /* if variable is binary (quite likely if an implication has been added) and occurs in a bilinear term, then mark that we should check implications */
      if( SCIPvarIsBinary(SCIPeventGetVar(event)) && consdata->quadvarterms[-varidx-1].nadjbilin > 0 )
         consdata->isimpladded = TRUE;
   }
#endif

   return SCIP_OKAY;
}

/** ensures, that linear vars and coefs arrays can store at least num entries */
static
SCIP_RETCODE consdataEnsureLinearVarsSize(
   SCIP*                 scip,               /**< SCIP data structure */
   SCIP_CONSDATA*        consdata,           /**< quadratic constraint data */
   int                   num                 /**< minimum number of entries to store */
   )
{
   assert(scip != NULL);
   assert(consdata != NULL);
   assert(consdata->nlinvars <= consdata->linvarssize);

   if( num > consdata->linvarssize )
   {
      int newsize;

      newsize = SCIPcalcMemGrowSize(scip, num);
      SCIP_CALL( SCIPreallocBlockMemoryArray(scip, &consdata->linvars,  consdata->linvarssize, newsize) );
      SCIP_CALL( SCIPreallocBlockMemoryArray(scip, &consdata->lincoefs, consdata->linvarssize, newsize) );
      if( consdata->lineventdata != NULL )
      {
         SCIP_CALL( SCIPreallocBlockMemoryArray(scip, &consdata->lineventdata, consdata->linvarssize, newsize) );
      }
      consdata->linvarssize = newsize;
   }
   assert(num <= consdata->linvarssize);

   return SCIP_OKAY;
}

/** ensures, that quadratic variable terms array can store at least num entries */
static
SCIP_RETCODE consdataEnsureQuadVarTermsSize(
   SCIP*                 scip,               /**< SCIP data structure */
   SCIP_CONSDATA*        consdata,           /**< quadratic constraint data */
   int                   num                 /**< minimum number of entries to store */
   )
{
   assert(scip != NULL);
   assert(consdata != NULL);
   assert(consdata->nquadvars <= consdata->quadvarssize);

   if( num > consdata->quadvarssize )
   {
      int newsize;

      newsize = SCIPcalcMemGrowSize(scip, num);
      SCIP_CALL( SCIPreallocBlockMemoryArray(scip, &consdata->quadvarterms, consdata->quadvarssize, newsize) );
      consdata->quadvarssize = newsize;
   }
   assert(num <= consdata->quadvarssize);

   return SCIP_OKAY;
}

/** ensures, that adjacency array can store at least num entries */
static
SCIP_RETCODE consdataEnsureAdjBilinSize(
   SCIP*                 scip,               /**< SCIP data structure */
   SCIP_QUADVARTERM*     quadvarterm,        /**< quadratic variable term */
   int                   num                 /**< minimum number of entries to store */
   )
{
   assert(scip != NULL);
   assert(quadvarterm != NULL);
   assert(quadvarterm->nadjbilin <= quadvarterm->adjbilinsize);

   if( num > quadvarterm->adjbilinsize )
   {
      int newsize;

      newsize = SCIPcalcMemGrowSize(scip, num);
      SCIP_CALL( SCIPreallocBlockMemoryArray(scip, &quadvarterm->adjbilin, quadvarterm->adjbilinsize, newsize) );
      quadvarterm->adjbilinsize = newsize;
   }
   assert(num <= quadvarterm->adjbilinsize);

   return SCIP_OKAY;
}

/** ensures, that bilinear term arrays can store at least num entries */
static
SCIP_RETCODE consdataEnsureBilinSize(
   SCIP*                 scip,               /**< SCIP data structure */
   SCIP_CONSDATA*        consdata,           /**< quadratic constraint data */
   int                   num                 /**< minimum number of entries to store */
   )
{
   assert(scip != NULL);
   assert(consdata != NULL);
   assert(consdata->nbilinterms <= consdata->bilintermssize);

   if( num > consdata->bilintermssize )
   {
      int newsize;

      newsize = SCIPcalcMemGrowSize(scip, num);
      SCIP_CALL( SCIPreallocBlockMemoryArray(scip, &consdata->bilinterms, consdata->bilintermssize, newsize) );
      consdata->bilintermssize = newsize;
   }
   assert(num <= consdata->bilintermssize);

   return SCIP_OKAY;
}

/** creates empty constraint data structure */
static
SCIP_RETCODE consdataCreateEmpty(
   SCIP*                 scip,               /**< SCIP data structure */
   SCIP_CONSDATA**       consdata            /**< a buffer to store pointer to new constraint data */
   )
{
   assert(scip != NULL);
   assert(consdata != NULL);

   SCIP_CALL( SCIPallocBlockMemory(scip, consdata) );
   BMSclearMemory(*consdata);

   (*consdata)->lhs = -SCIPinfinity(scip);
   (*consdata)->rhs =  SCIPinfinity(scip);

   (*consdata)->linvarssorted  = TRUE;
   (*consdata)->linvarsmerged  = TRUE;
   (*consdata)->quadvarssorted = TRUE;
   (*consdata)->quadvarsmerged = TRUE;
   (*consdata)->bilinsorted    = TRUE;
   (*consdata)->bilinmerged    = TRUE;

   (*consdata)->isremovedfixings = TRUE;
   (*consdata)->ispropagated     = TRUE;
   (*consdata)->initialmerge     = FALSE;

   (*consdata)->linvar_maydecrease = -1;
   (*consdata)->linvar_mayincrease = -1;

   (*consdata)->minlinactivity = SCIP_INVALID;
   (*consdata)->maxlinactivity = SCIP_INVALID;
   (*consdata)->minlinactivityinf = -1;
   (*consdata)->maxlinactivityinf = -1;

   return SCIP_OKAY;
}

/** creates constraint data structure */
static
SCIP_RETCODE consdataCreate(
   SCIP*                 scip,               /**< SCIP data structure */
   SCIP_CONSDATA**       consdata,           /**< a buffer to store pointer to new constraint data */
   SCIP_Real             lhs,                /**< left hand side of constraint */
   SCIP_Real             rhs,                /**< right hand side of constraint */
   int                   nlinvars,           /**< number of linear variables */
   SCIP_VAR**            linvars,            /**< array of linear variables */
   SCIP_Real*            lincoefs,           /**< array of coefficients of linear variables */
   int                   nquadvars,          /**< number of quadratic variables */
   SCIP_QUADVARTERM*     quadvarterms,       /**< array of quadratic variable terms */
   int                   nbilinterms,        /**< number of bilinear terms */
   SCIP_BILINTERM*       bilinterms,         /**< array of bilinear terms */
   SCIP_Bool             capturevars         /**< whether we should capture variables */
   )
{
   int i;

   assert(scip != NULL);
   assert(consdata != NULL);

   assert(nlinvars == 0 || linvars  != NULL);
   assert(nlinvars == 0 || lincoefs != NULL);
   assert(nquadvars == 0 || quadvarterms != NULL);
   assert(nbilinterms == 0 || bilinterms != NULL);

   SCIP_CALL( SCIPallocBlockMemory(scip, consdata) );
   BMSclearMemory(*consdata);

   (*consdata)->minlinactivity = SCIP_INVALID;
   (*consdata)->maxlinactivity = SCIP_INVALID;
   (*consdata)->minlinactivityinf = -1;
   (*consdata)->maxlinactivityinf = -1;

   (*consdata)->lhs = lhs;
   (*consdata)->rhs = rhs;

   if( nlinvars > 0 )
   {
      SCIP_CALL( SCIPduplicateBlockMemoryArray(scip, &(*consdata)->linvars,  linvars,  nlinvars) );
      SCIP_CALL( SCIPduplicateBlockMemoryArray(scip, &(*consdata)->lincoefs, lincoefs, nlinvars) );
      (*consdata)->nlinvars = nlinvars;
      (*consdata)->linvarssize = nlinvars;

      if( capturevars )
         for( i = 0; i < nlinvars; ++i )
         {
            SCIP_CALL( SCIPcaptureVar(scip, linvars[i]) );
         }
   }
   else
   {
      (*consdata)->linvarssorted = TRUE;
      (*consdata)->linvarsmerged = TRUE;
      (*consdata)->minlinactivity = 0.0;
      (*consdata)->maxlinactivity = 0.0;
      (*consdata)->minlinactivityinf = 0;
      (*consdata)->maxlinactivityinf = 0;
   }

   if( nquadvars > 0 )
   {
      SCIP_CALL( SCIPduplicateBlockMemoryArray(scip, &(*consdata)->quadvarterms, quadvarterms, nquadvars) );

      for( i = 0; i < nquadvars; ++i )
      {
         (*consdata)->quadvarterms[i].eventdata = NULL;
         if( quadvarterms[i].nadjbilin )
         {
            SCIP_CALL( SCIPduplicateBlockMemoryArray(scip, &(*consdata)->quadvarterms[i].adjbilin, quadvarterms[i].adjbilin, quadvarterms[i].nadjbilin) );
            (*consdata)->quadvarterms[i].adjbilinsize = quadvarterms[i].nadjbilin;
         }
         else
         {
            assert((*consdata)->quadvarterms[i].nadjbilin == 0);
            (*consdata)->quadvarterms[i].adjbilin = NULL;
            (*consdata)->quadvarterms[i].adjbilinsize = 0;
         }
         if( capturevars )
         {
            SCIP_CALL( SCIPcaptureVar(scip, quadvarterms[i].var) );
         }
      }

      (*consdata)->nquadvars = nquadvars;
      (*consdata)->quadvarssize = nquadvars;
      SCIPintervalSetEmpty(&(*consdata)->quadactivitybounds);
   }
   else
   {
      (*consdata)->quadvarssorted = TRUE;
      (*consdata)->quadvarsmerged = TRUE;
      SCIPintervalSet(&(*consdata)->quadactivitybounds, 0.0);
   }

   if( nbilinterms > 0 )
   {
      SCIP_CALL( SCIPduplicateBlockMemoryArray(scip, &(*consdata)->bilinterms, bilinterms, nbilinterms) );
      (*consdata)->nbilinterms = nbilinterms;
      (*consdata)->bilintermssize = nbilinterms;
   }
   else
   {
      (*consdata)->bilinsorted = TRUE;
      (*consdata)->bilinmerged = TRUE;
   }

   (*consdata)->linvar_maydecrease = -1;
   (*consdata)->linvar_mayincrease = -1;

   (*consdata)->activity = SCIP_INVALID;
   (*consdata)->lhsviol  = SCIPisInfinity(scip, -lhs) ? 0.0 : SCIP_INVALID;
   (*consdata)->rhsviol  = SCIPisInfinity(scip,  rhs) ? 0.0 : SCIP_INVALID;

   return SCIP_OKAY;
}

/** frees constraint data structure */
static
SCIP_RETCODE consdataFree(
   SCIP*                 scip,               /**< SCIP data structure */
   SCIP_CONSDATA**       consdata            /**< pointer to constraint data to free */
   )
{
   int i;

   assert(scip != NULL);
   assert(consdata != NULL);
   assert(*consdata != NULL);

   /* free sepa arrays, may exists if constraint is deleted in solving stage */
   SCIPfreeBlockMemoryArrayNull(scip, &(*consdata)->sepaquadvars,     (*consdata)->nquadvars);
   SCIPfreeBlockMemoryArrayNull(scip, &(*consdata)->sepabilinvar2pos, (*consdata)->nbilinterms);

   /* release linear variables and free linear part */
   if( (*consdata)->linvarssize > 0 )
   {
      for( i = 0; i < (*consdata)->nlinvars; ++i )
      {
         assert((*consdata)->lineventdata == NULL || (*consdata)->lineventdata[i] == NULL); /* variable events should have been dropped earlier */
         SCIP_CALL( SCIPreleaseVar(scip, &(*consdata)->linvars[i]) );
      }
      SCIPfreeBlockMemoryArray(scip, &(*consdata)->linvars,  (*consdata)->linvarssize);
      SCIPfreeBlockMemoryArray(scip, &(*consdata)->lincoefs, (*consdata)->linvarssize);
      SCIPfreeBlockMemoryArrayNull(scip, &(*consdata)->lineventdata, (*consdata)->linvarssize);
   }
   assert((*consdata)->linvars == NULL);
   assert((*consdata)->lincoefs == NULL);
   assert((*consdata)->lineventdata == NULL);

   /* release quadratic variables and free quadratic variable term part */
   for( i = 0; i < (*consdata)->nquadvars; ++i )
   {
      assert((*consdata)->quadvarterms[i].eventdata == NULL); /* variable events should have been dropped earlier */
      SCIPfreeBlockMemoryArrayNull(scip, &(*consdata)->quadvarterms[i].adjbilin, (*consdata)->quadvarterms[i].adjbilinsize);
      SCIP_CALL( SCIPreleaseVar(scip, &(*consdata)->quadvarterms[i].var) );
   }
   SCIPfreeBlockMemoryArrayNull(scip, &(*consdata)->quadvarterms, (*consdata)->quadvarssize);

   /* free bilinear terms */
   SCIPfreeBlockMemoryArrayNull(scip, &(*consdata)->bilinterms, (*consdata)->bilintermssize);

   /* free nonlinear row representation */
   if( (*consdata)->nlrow != NULL )
   {
      SCIP_CALL( SCIPreleaseNlRow(scip, &(*consdata)->nlrow) );
   }

   SCIPfreeBlockMemory(scip, consdata);
   *consdata = NULL;

   return SCIP_OKAY;
}

/** sorts linear part of constraint data */
static
void consdataSortLinearVars(
   SCIP_CONSDATA*        consdata            /**< quadratic constraint data */
   )
{
   assert(consdata != NULL);

   if( consdata->linvarssorted )
      return;

   if( consdata->nlinvars <= 1 )
   {
      consdata->linvarssorted = TRUE;
      return;
   }

   if( consdata->lineventdata == NULL )
   {
      SCIPsortPtrReal((void**)consdata->linvars, consdata->lincoefs, SCIPvarComp, consdata->nlinvars);
   }
   else
   {
      int i;

      SCIPsortPtrPtrReal((void**)consdata->linvars, (void**)consdata->lineventdata, consdata->lincoefs, SCIPvarComp, consdata->nlinvars);

      /* update variable indices in event data */
      for( i = 0; i < consdata->nlinvars; ++i )
         if( consdata->lineventdata[i] != NULL )
            consdata->lineventdata[i]->varidx = i;
   }

   consdata->linvarssorted = TRUE;
}

#ifdef SCIP_DISABLED_CODE /* no-one needs this routine currently */
/** returns the position of variable in the linear coefficients array of a constraint, or -1 if not found */
static
int consdataFindLinearVar(
   SCIP_CONSDATA*        consdata,           /**< quadratic constraint data */
   SCIP_VAR*             var                 /**< variable to search for */
   )
{
   int pos;

   assert(consdata != NULL);
   assert(var != NULL);

   if( consdata->nlinvars == 0 )
      return -1;

   consdataSortLinearVars(consdata);

   if( !SCIPsortedvecFindPtr((void**)consdata->linvars, SCIPvarComp, (void*)var, consdata->nlinvars, &pos) )
      pos = -1;

   return pos;
}
#endif

/** index comparison method for quadratic variable terms: compares two indices of the quadratic variable set in the quadratic constraint */
static
SCIP_DECL_SORTINDCOMP(quadVarTermComp)
{  /*lint --e{715}*/
   SCIP_CONSDATA* consdata = (SCIP_CONSDATA*)dataptr;

   assert(consdata != NULL);
   assert(0 <= ind1 && ind1 < consdata->nquadvars);
   assert(0 <= ind2 && ind2 < consdata->nquadvars);

   return SCIPvarCompare(consdata->quadvarterms[ind1].var, consdata->quadvarterms[ind2].var);
}

/** sorting of quadratic variable terms */
static
SCIP_RETCODE consdataSortQuadVarTerms(
   SCIP*                 scip,               /**< SCIP data structure */
   SCIP_CONSDATA*        consdata            /**< quadratic constraint data */
   )
{
   int* perm;
   int  i;
   int  nexti;
   int  v;
   SCIP_QUADVARTERM quadterm;

   assert(scip != NULL);
   assert(consdata != NULL);

   if( consdata->quadvarssorted )
      return SCIP_OKAY;

   if( consdata->nquadvars == 0 )
   {
      consdata->quadvarssorted = TRUE;
      return SCIP_OKAY;
   }

   /* get temporary memory to store the sorted permutation */
   SCIP_CALL( SCIPallocBufferArray(scip, &perm, consdata->nquadvars) );

   /* call bubble sort */
   SCIPsort(perm, quadVarTermComp, (void*)consdata, consdata->nquadvars);

   /* permute the quadratic variable terms according to the resulting permutation */
   for( v = 0; v < consdata->nquadvars; ++v )
   {
      if( perm[v] != v )
      {
         quadterm = consdata->quadvarterms[v];

         i = v;
         do
         {
            assert(0 <= perm[i] && perm[i] < consdata->nquadvars);
            assert(perm[i] != i);
            consdata->quadvarterms[i] = consdata->quadvarterms[perm[i]];
            if( consdata->quadvarterms[i].eventdata != NULL )
            {
               consdata->quadvarterms[i].eventdata->varidx = -i-1;
            }
            nexti = perm[i];
            perm[i] = i;
            i = nexti;
         }
         while( perm[i] != v );
         consdata->quadvarterms[i] = quadterm;
         if( consdata->quadvarterms[i].eventdata != NULL )
         {
            consdata->quadvarterms[i].eventdata->varidx = -i-1;
         }
         perm[i] = i;
      }
   }
   consdata->quadvarssorted = TRUE;

   /* free temporary memory */
   SCIPfreeBufferArray(scip, &perm);

   return SCIP_OKAY;
}

/** returns the position of variable in the quadratic variable terms array of a constraint, or -1 if not found */
static
SCIP_RETCODE consdataFindQuadVarTerm(
   SCIP*                 scip,               /**< SCIP data structure */
   SCIP_CONSDATA*        consdata,           /**< quadratic constraint data */
   SCIP_VAR*             var,                /**< variable to search for */
   int*                  pos                 /**< buffer where to store position of var in quadvarterms array, or -1 if not found */
   )
{
   int left;
   int right;
   int cmpres;

   assert(consdata != NULL);
   assert(var != NULL);
   assert(pos != NULL);

   if( consdata->nquadvars == 0 )
   {
      *pos = -1;
      return SCIP_OKAY;
   }

   SCIP_CALL( consdataSortQuadVarTerms(scip, consdata) );

   left = 0;
   right = consdata->nquadvars - 1;
   while( left <= right )
   {
      int middle;

      middle = (left+right)/2;
      assert(0 <= middle && middle < consdata->nquadvars);

      cmpres = SCIPvarCompare(var, consdata->quadvarterms[middle].var);

      if( cmpres < 0 )
         right = middle - 1;
      else if( cmpres > 0 )
         left  = middle + 1;
      else
      {
         *pos = middle;
         return SCIP_OKAY;
      }
   }
   assert(left == right+1);

   *pos = -1;

   return SCIP_OKAY;
}

/** index comparison method for bilinear terms: compares two index pairs of the bilinear term set in the quadratic constraint */
static
SCIP_DECL_SORTINDCOMP(bilinTermComp)
{  /*lint --e{715}*/
   SCIP_CONSDATA* consdata = (SCIP_CONSDATA*)dataptr;
   int var1cmp;

   assert(consdata != NULL);
   assert(0 <= ind1 && ind1 < consdata->nbilinterms);
   assert(0 <= ind2 && ind2 < consdata->nbilinterms);

   var1cmp = SCIPvarCompare(consdata->bilinterms[ind1].var1, consdata->bilinterms[ind2].var1);
   if( var1cmp != 0 )
      return var1cmp;

   return SCIPvarCompare(consdata->bilinterms[ind1].var2, consdata->bilinterms[ind2].var2);
}

/** sorting of bilinear terms */
static
SCIP_RETCODE consdataSortBilinTerms(
   SCIP*                 scip,               /**< SCIP data structure */
   SCIP_CONSDATA*        consdata            /**< quadratic constraint data */
   )
{
   int* perm;
   int* invperm;
   int  i;
   int  nexti;
   int  v;
   SCIP_BILINTERM bilinterm;

   assert(scip != NULL);
   assert(consdata != NULL);

   if( consdata->bilinsorted )
      return SCIP_OKAY;

   if( consdata->nbilinterms == 0 )
   {
      consdata->bilinsorted = TRUE;
      return SCIP_OKAY;
   }

   /* get temporary memory to store the sorted permutation and the inverse permutation */
   SCIP_CALL( SCIPallocBufferArray(scip, &perm,    consdata->nbilinterms) );
   SCIP_CALL( SCIPallocBufferArray(scip, &invperm, consdata->nbilinterms) );

   /* call bubble sort */
   SCIPsort(perm, bilinTermComp, (void*)consdata, consdata->nbilinterms);

   /* compute inverted permutation */
   for( v = 0; v < consdata->nbilinterms; ++v )
   {
      assert(0 <= perm[v] && perm[v] < consdata->nbilinterms);
      invperm[perm[v]] = v;
   }

   /* permute the bilinear terms according to the resulting permutation */
   for( v = 0; v < consdata->nbilinterms; ++v )
   {
      if( perm[v] != v )
      {
         bilinterm = consdata->bilinterms[v];

         i = v;
         do
         {
            assert(0 <= perm[i] && perm[i] < consdata->nbilinterms);
            assert(perm[i] != i);
            consdata->bilinterms[i] = consdata->bilinterms[perm[i]];
            nexti = perm[i];
            perm[i] = i;
            i = nexti;
         }
         while( perm[i] != v );
         consdata->bilinterms[i] = bilinterm;
         perm[i] = i;
      }
   }

   /* update the adjacency information in the quadratic variable terms */
   for( v = 0; v < consdata->nquadvars; ++v )
      for( i = 0; i < consdata->quadvarterms[v].nadjbilin; ++i )
         consdata->quadvarterms[v].adjbilin[i] = invperm[consdata->quadvarterms[v].adjbilin[i]];

   consdata->bilinsorted = TRUE;

   /* free temporary memory */
   SCIPfreeBufferArray(scip, &perm);
   SCIPfreeBufferArray(scip, &invperm);

   return SCIP_OKAY;
}

/** moves a linear variable from one position to another */
static
void consdataMoveLinearVar(
   SCIP_CONSDATA*        consdata,           /**< constraint data */
   int                   oldpos,             /**< position of variable that shall be moved */
   int                   newpos              /**< new position of variable */
   )
{
   assert(consdata != NULL);
   assert(oldpos >= 0);
   assert(oldpos < consdata->nlinvars);
   assert(newpos >= 0);
   assert(newpos < consdata->linvarssize);

   if( newpos == oldpos )
      return;

   consdata->linvars [newpos] = consdata->linvars [oldpos];
   consdata->lincoefs[newpos] = consdata->lincoefs[oldpos];

   if( consdata->lineventdata != NULL )
   {
      assert(newpos >= consdata->nlinvars || consdata->lineventdata[newpos] == NULL);

      consdata->lineventdata[newpos] = consdata->lineventdata[oldpos];
      consdata->lineventdata[newpos]->varidx = newpos;

      consdata->lineventdata[oldpos] = NULL;
   }

   consdata->linvarssorted = FALSE;
}   

/** moves a quadratic variable from one position to another */
static
void consdataMoveQuadVarTerm(
   SCIP_CONSDATA*        consdata,           /**< constraint data */
   int                   oldpos,             /**< position of variable that shall be moved */
   int                   newpos              /**< new position of variable */
   )
{
   assert(consdata != NULL);
   assert(oldpos >= 0);
   assert(oldpos < consdata->nquadvars);
   assert(newpos >= 0);
   assert(newpos < consdata->quadvarssize);

   if( newpos == oldpos )
      return;

   assert(newpos >= consdata->nquadvars || consdata->quadvarterms[newpos].eventdata == NULL);

   consdata->quadvarterms[newpos] = consdata->quadvarterms[oldpos];

   if( consdata->quadvarterms[newpos].eventdata != NULL )
   {
      consdata->quadvarterms[newpos].eventdata->varidx = -newpos-1;
      consdata->quadvarterms[oldpos].eventdata = NULL;
   }

   consdata->quadvarssorted = FALSE;
}   

/** adds linear coefficient in quadratic constraint */
static
SCIP_RETCODE addLinearCoef(
   SCIP*                 scip,               /**< SCIP data structure */
   SCIP_CONS*            cons,               /**< quadratic constraint */
   SCIP_VAR*             var,                /**< variable of constraint entry */
   SCIP_Real             coef                /**< coefficient of constraint entry */
   )
{
   SCIP_CONSDATA* consdata;
   SCIP_Bool transformed;

   assert(scip != NULL);
   assert(cons != NULL);
   assert(var  != NULL);

   /* ignore coefficient if it is nearly zero */
   if( SCIPisZero(scip, coef) )
      return SCIP_OKAY;

   consdata = SCIPconsGetData(cons);
   assert(consdata != NULL);

   /* are we in the transformed problem? */
   transformed = SCIPconsIsTransformed(cons);

   /* always use transformed variables in transformed constraints */
   if( transformed )
   {
      SCIP_CALL( SCIPgetTransformedVar(scip, var, &var) );
   }
   assert(var != NULL);
   assert(transformed == SCIPvarIsTransformed(var));

   SCIP_CALL( consdataEnsureLinearVarsSize(scip, consdata, consdata->nlinvars+1) );
   consdata->linvars [consdata->nlinvars] = var;
   consdata->lincoefs[consdata->nlinvars] = coef;

   ++consdata->nlinvars;

   /* catch variable events */
   if( consdata->lineventdata != NULL )
   {
      SCIP_CONSHDLR* conshdlr;
      SCIP_CONSHDLRDATA* conshdlrdata;

      /* get event handler */
      conshdlr = SCIPconsGetHdlr(cons);
      conshdlrdata = SCIPconshdlrGetData(conshdlr);
      assert(conshdlrdata != NULL);
      assert(conshdlrdata->eventhdlr != NULL);

      consdata->lineventdata[consdata->nlinvars-1] = NULL;

      /* catch bound change events of variable */
      SCIP_CALL( catchLinearVarEvents(scip, conshdlrdata->eventhdlr, cons, consdata->nlinvars-1) );
   }

   /* invalidate activity information */
   consdata->activity = SCIP_INVALID;
   consdata->minlinactivity = SCIP_INVALID;
   consdata->maxlinactivity = SCIP_INVALID;
   consdata->minlinactivityinf = -1;
   consdata->maxlinactivityinf = -1;

   /* invalidate nonlinear row */
   if( consdata->nlrow != NULL )
   {
      SCIP_CALL( SCIPreleaseNlRow(scip, &consdata->nlrow) );
   }

   /* install rounding locks for new variable */
   SCIP_CALL( lockLinearVariable(scip, cons, var, coef) );

   /* capture new variable */
   SCIP_CALL( SCIPcaptureVar(scip, var) );

   consdata->ispropagated = FALSE;
   consdata->ispresolved = FALSE;
   consdata->isremovedfixings = consdata->isremovedfixings && SCIPvarIsActive(var);
   if( consdata->nlinvars == 1 )
      consdata->linvarssorted = TRUE;
   else
      consdata->linvarssorted = consdata->linvarssorted && (SCIPvarCompare(consdata->linvars[consdata->nlinvars-2], consdata->linvars[consdata->nlinvars-1]) == -1);
   /* always set too FALSE since the new linear variable should be checked if already existing as quad var term */ 
   consdata->linvarsmerged = FALSE;

   return SCIP_OKAY;
}

/** deletes linear coefficient at given position from quadratic constraint data */
static
SCIP_RETCODE delLinearCoefPos(
   SCIP*                 scip,               /**< SCIP data structure */
   SCIP_CONS*            cons,               /**< quadratic constraint */
   int                   pos                 /**< position of coefficient to delete */
   )
{
   SCIP_CONSDATA* consdata;
   SCIP_VAR* var;
   SCIP_Real coef;

   assert(scip != NULL);
   assert(cons != NULL);

   consdata = SCIPconsGetData(cons);
   assert(consdata != NULL);
   assert(0 <= pos && pos < consdata->nlinvars);

   var  = consdata->linvars[pos];
   coef = consdata->lincoefs[pos];
   assert(var != NULL);

   /* remove rounding locks for deleted variable */
   SCIP_CALL( unlockLinearVariable(scip, cons, var, coef) );

   /* if we catch variable events, drop the events on the variable */
   if( consdata->lineventdata != NULL )
   {
      SCIP_CONSHDLR* conshdlr;
      SCIP_CONSHDLRDATA* conshdlrdata;

      /* get event handler */
      conshdlr = SCIPconsGetHdlr(cons);
      conshdlrdata = SCIPconshdlrGetData(conshdlr);
      assert(conshdlrdata != NULL);
      assert(conshdlrdata->eventhdlr != NULL);

      /* drop bound change events of variable */
      SCIP_CALL( dropLinearVarEvents(scip, conshdlrdata->eventhdlr, cons, pos) );
   }

   /* release variable */
   SCIP_CALL( SCIPreleaseVar(scip, &consdata->linvars[pos]) );

   /* move the last variable to the free slot */
   consdataMoveLinearVar(consdata, consdata->nlinvars-1, pos);

   --consdata->nlinvars;

   /* invalidate activity */
   consdata->activity = SCIP_INVALID;
   consdata->minlinactivity = SCIP_INVALID;
   consdata->maxlinactivity = SCIP_INVALID;
   consdata->minlinactivityinf = -1;
   consdata->maxlinactivityinf = -1;

   /* invalidate nonlinear row */
   if( consdata->nlrow != NULL )
   {
      SCIP_CALL( SCIPreleaseNlRow(scip, &consdata->nlrow) );
   }

   consdata->ispropagated = FALSE;
   consdata->ispresolved  = FALSE;

   return SCIP_OKAY;
}

/** changes linear coefficient value at given position of quadratic constraint */
static
SCIP_RETCODE chgLinearCoefPos(
   SCIP*                 scip,               /**< SCIP data structure */
   SCIP_CONS*            cons,               /**< quadratic constraint */
   int                   pos,                /**< position of linear coefficient to change */
   SCIP_Real             newcoef             /**< new value of linear coefficient */
   )
{
   SCIP_CONSHDLR* conshdlr;
   SCIP_CONSHDLRDATA* conshdlrdata;
   SCIP_CONSDATA* consdata;
   SCIP_VAR* var;
   SCIP_Real coef;

   assert(scip != NULL);
   assert(cons != NULL);
   assert(!SCIPisZero(scip, newcoef));

   conshdlrdata = NULL;

   consdata = SCIPconsGetData(cons);
   assert(consdata != NULL);
   assert(0 <= pos);
   assert(pos < consdata->nlinvars);
   assert(!SCIPisZero(scip, newcoef));

   var = consdata->linvars[pos];
   coef = consdata->lincoefs[pos];
   assert(var != NULL);
   assert(SCIPconsIsTransformed(cons) == SCIPvarIsTransformed(var));

   /* invalidate activity */
   consdata->activity = SCIP_INVALID;
   consdata->minlinactivity = SCIP_INVALID;
   consdata->maxlinactivity = SCIP_INVALID;
   consdata->minlinactivityinf = -1;
   consdata->maxlinactivityinf = -1;

   /* invalidate nonlinear row */
   if( consdata->nlrow != NULL )
   {
      SCIP_CALL( SCIPreleaseNlRow(scip, &consdata->nlrow) );
   }

   /* if necessary, remove the rounding locks and event catching of the variable */
   if( newcoef * coef < 0.0 )
   {
      if( SCIPconsIsLocked(cons) )
      {
         assert(SCIPconsIsTransformed(cons));

         /* remove rounding locks for variable with old coefficient */
         SCIP_CALL( unlockLinearVariable(scip, cons, var, coef) );
      }

      if( consdata->lineventdata[pos] != NULL )
      {
         /* get event handler */
         conshdlr = SCIPconsGetHdlr(cons);
         conshdlrdata = SCIPconshdlrGetData(conshdlr);
         assert(conshdlrdata != NULL);
         assert(conshdlrdata->eventhdlr != NULL);

         /* drop bound change events of variable */
         SCIP_CALL( dropLinearVarEvents(scip, conshdlrdata->eventhdlr, cons, pos) );
      }
   }

   /* change the coefficient */
   consdata->lincoefs[pos] = newcoef;

   /* if necessary, install the rounding locks and event catching of the variable again */
   if( newcoef * coef < 0.0 )
   {
      if( SCIPconsIsLocked(cons) )
      {
         /* install rounding locks for variable with new coefficient */
         SCIP_CALL( lockLinearVariable(scip, cons, var, newcoef) );
      }

      if( conshdlrdata != NULL )
      {
         /* catch bound change events of variable */
         SCIP_CALL( catchLinearVarEvents(scip, conshdlrdata->eventhdlr, cons, pos) );
      }
   }

   consdata->ispropagated = FALSE;
   consdata->ispresolved = FALSE;

   return SCIP_OKAY;
}

/** adds quadratic variable term to quadratic constraint */
static
SCIP_RETCODE addQuadVarTerm(
   SCIP*                 scip,               /**< SCIP data structure */
   SCIP_CONS*            cons,               /**< quadratic constraint */
   SCIP_VAR*             var,                /**< variable to add */
   SCIP_Real             lincoef,            /**< linear coefficient of variable */
   SCIP_Real             sqrcoef,            /**< square coefficient of variable */
   SCIP_Bool             catchevents         /**< whether we should catch variable events */
   )
{
   SCIP_CONSDATA* consdata;
   SCIP_Bool transformed;
   SCIP_QUADVARTERM* quadvarterm;

   assert(scip != NULL);
   assert(cons != NULL);
   assert(var  != NULL);

   consdata = SCIPconsGetData(cons);
   assert(consdata != NULL);

   /* are we in the transformed problem? */
   transformed = SCIPconsIsTransformed(cons);

   /* always use transformed variables in transformed constraints */
   if( transformed )
   {
      SCIP_CALL( SCIPgetTransformedVar(scip, var, &var) );
   }
   assert(var != NULL);
   assert(transformed == SCIPvarIsTransformed(var));

   SCIP_CALL( consdataEnsureQuadVarTermsSize(scip, consdata, consdata->nquadvars+1) );

   quadvarterm = &consdata->quadvarterms[consdata->nquadvars];
   quadvarterm->var       = var;
   quadvarterm->lincoef   = lincoef;
   quadvarterm->sqrcoef   = sqrcoef;
   quadvarterm->adjbilinsize = 0;
   quadvarterm->nadjbilin = 0;
   quadvarterm->adjbilin  = NULL;
   quadvarterm->eventdata = NULL;

   ++consdata->nquadvars;

   /* capture variable */
   SCIP_CALL( SCIPcaptureVar(scip, var) );

   /* catch variable events, if we do so */
   if( catchevents )
   {
      SCIP_CONSHDLR* conshdlr;
      SCIP_CONSHDLRDATA* conshdlrdata;

      /* get event handler */
      conshdlr = SCIPconsGetHdlr(cons);
      conshdlrdata = SCIPconshdlrGetData(conshdlr);
      assert(conshdlrdata != NULL);
      assert(conshdlrdata->eventhdlr != NULL);

      /* catch bound change events of variable */
      SCIP_CALL( catchQuadVarEvents(scip, conshdlrdata->eventhdlr, cons, consdata->nquadvars-1) );
   }

   /* invalidate activity information */
   consdata->activity = SCIP_INVALID;
   SCIPintervalSetEmpty(&consdata->quadactivitybounds);

   /* invalidate nonlinear row */
   if( consdata->nlrow != NULL )
   {
      SCIP_CALL( SCIPreleaseNlRow(scip, &consdata->nlrow) );
   }

   /* install rounding locks for new variable */
   SCIP_CALL( lockQuadraticVariable(scip, cons, var) );

   consdata->ispropagated = FALSE;
   consdata->ispresolved  = FALSE;
   consdata->isremovedfixings = consdata->isremovedfixings && SCIPvarIsActive(var);
   if( consdata->nquadvars == 1 )
      consdata->quadvarssorted = TRUE;
   else
      consdata->quadvarssorted = consdata->quadvarssorted && (SCIPvarCompare(consdata->quadvarterms[consdata->nquadvars-2].var, consdata->quadvarterms[consdata->nquadvars-1].var) == -1);
   /* also set to FALSE if nquadvars == 1, since the new variable should be checked for linearity and other stuff in mergeAndClean ... */ 
   consdata->quadvarsmerged = FALSE;

   consdata->iscurvchecked = FALSE;

   return SCIP_OKAY;
}

/** deletes quadratic variable term at given position from quadratic constraint data */
static
SCIP_RETCODE delQuadVarTermPos(
   SCIP*                 scip,               /**< SCIP data structure */
   SCIP_CONS*            cons,               /**< quadratic constraint */
   int                   pos                 /**< position of term to delete */
   )
{
   SCIP_CONSDATA* consdata;
   SCIP_VAR* var;

   assert(scip != NULL);
   assert(cons != NULL);

   consdata = SCIPconsGetData(cons);
   assert(consdata != NULL);
   assert(0 <= pos && pos < consdata->nquadvars);

   var = consdata->quadvarterms[pos].var;
   assert(var != NULL);
   assert(consdata->quadvarterms[pos].nadjbilin == 0);

   /* remove rounding locks for deleted variable */
   SCIP_CALL( unlockQuadraticVariable(scip, cons, var) );

   /* if we catch variable events, drop the events on the variable */
   if( consdata->quadvarterms[pos].eventdata != NULL )
   {
      SCIP_CONSHDLR* conshdlr;
      SCIP_CONSHDLRDATA* conshdlrdata;

      /* get event handler */
      conshdlr = SCIPconsGetHdlr(cons);
      conshdlrdata = SCIPconshdlrGetData(conshdlr);
      assert(conshdlrdata != NULL);
      assert(conshdlrdata->eventhdlr != NULL);

      /* drop bound change events of variable */
      SCIP_CALL( dropQuadVarEvents(scip, conshdlrdata->eventhdlr, cons, pos) );
   }

   /* release variable */
   SCIP_CALL( SCIPreleaseVar(scip, &consdata->quadvarterms[pos].var) );

   /* free adjacency array */
   SCIPfreeBlockMemoryArrayNull(scip, &consdata->quadvarterms[pos].adjbilin, consdata->quadvarterms[pos].adjbilinsize);

   /* move the last variable term to the free slot */
   consdataMoveQuadVarTerm(consdata, consdata->nquadvars-1, pos);

   --consdata->nquadvars;

   /* invalidate activity */
   consdata->activity = SCIP_INVALID;
   SCIPintervalSetEmpty(&consdata->quadactivitybounds);

   /* invalidate nonlinear row */
   if( consdata->nlrow != NULL )
   {
      SCIP_CALL( SCIPreleaseNlRow(scip, &consdata->nlrow) );
   }

   consdata->ispropagated  = FALSE;
   consdata->ispresolved   = FALSE;
   consdata->iscurvchecked = FALSE;

   return SCIP_OKAY;
}

/** replace variable in quadratic variable term at given position of quadratic constraint data 
 * allows to replace x by coef*y+offset, thereby maintaining linear and square coefficients and bilinear terms */
static
SCIP_RETCODE replaceQuadVarTermPos(
   SCIP*                 scip,               /**< SCIP data structure */
   SCIP_CONS*            cons,               /**< quadratic constraint */
   int                   pos,                /**< position of term to replace */
   SCIP_VAR*             var,                /**< new variable */
   SCIP_Real             coef,               /**< linear coefficient of new variable */
   SCIP_Real             offset              /**< offset of new variable */
   )
{
   SCIP_CONSDATA* consdata;
   SCIP_QUADVARTERM* quadvarterm;
   SCIP_EVENTHDLR* eventhdlr;
   SCIP_BILINTERM* bilinterm;
   SCIP_Real constant;

   int i;
   SCIP_VAR* var2;

   consdata = SCIPconsGetData(cons);
   assert(consdata != NULL);
   assert(pos >= 0);
   assert(pos <  consdata->nquadvars);

   quadvarterm = &consdata->quadvarterms[pos];

   /* remove rounding locks for old variable */
   SCIP_CALL( unlockQuadraticVariable(scip, cons, quadvarterm->var) );

   /* if we catch variable events, drop the events on the old variable */
   if( quadvarterm->eventdata != NULL )
   {
      SCIP_CONSHDLR* conshdlr;
      SCIP_CONSHDLRDATA* conshdlrdata;

      /* get event handler */
      conshdlr = SCIPconsGetHdlr(cons);
      conshdlrdata = SCIPconshdlrGetData(conshdlr);
      assert(conshdlrdata != NULL);
      assert(conshdlrdata->eventhdlr != NULL);

      eventhdlr = conshdlrdata->eventhdlr;

      /* drop bound change events of variable */
      SCIP_CALL( dropQuadVarEvents(scip, eventhdlr, cons, pos) );
   }
   else
   {
      eventhdlr = NULL;
   }

   /* compute constant and put into lhs/rhs */
   constant = quadvarterm->lincoef * offset + quadvarterm->sqrcoef * offset * offset;
   if( constant != 0.0 )
   {
      /* maintain constant part */
      if( !SCIPisInfinity(scip, -consdata->lhs) )
         consdata->lhs -= constant;
      if( !SCIPisInfinity(scip,  consdata->rhs) )
         consdata->rhs -= constant;
   }

   /* update linear and square coefficient */
   quadvarterm->lincoef *= coef;
   quadvarterm->lincoef += 2.0 * quadvarterm->sqrcoef * coef * offset;
   quadvarterm->sqrcoef *= coef * coef;

   /* update bilinear terms */
   for( i = 0; i < quadvarterm->nadjbilin; ++i )
   {
      bilinterm = &consdata->bilinterms[quadvarterm->adjbilin[i]];

      if( bilinterm->var1 == quadvarterm->var )
      {
         bilinterm->var1 = var;
         var2 = bilinterm->var2;
      }
      else
      {
         assert(bilinterm->var2 == quadvarterm->var);
         bilinterm->var2 = var;
         var2 = bilinterm->var1;
      }

      if( var == var2 )
      {
         /* looks like we actually have a square term here */
         quadvarterm->lincoef += bilinterm->coef * offset;
         quadvarterm->sqrcoef += bilinterm->coef * coef;
         /* deleting bilinear terms is expensive, since it requires updating adjacency information
          * thus, for now we just set the coefficient to 0.0 and clear in later when the bilinear terms are merged */
         bilinterm->coef = 0.0;
         continue;
      }

      /* swap var1 and var2 if they are in wrong order */
      if( SCIPvarCompare(bilinterm->var1, bilinterm->var2) > 0 )
      {
         SCIP_VAR* tmp;
         tmp = bilinterm->var1;
         bilinterm->var1 = bilinterm->var2;
         bilinterm->var2 = tmp;
      }
      assert(SCIPvarCompare(bilinterm->var1, bilinterm->var2) == -1);

      if( offset != 0.0 )
      {
         /* need to find var2 and add offset*bilinterm->coef to linear coefficient */
         int var2pos;

         var2pos = 0;
         while( consdata->quadvarterms[var2pos].var != var2 )
         {
            ++var2pos;
            assert(var2pos < consdata->nquadvars);
         }

         consdata->quadvarterms[var2pos].lincoef += bilinterm->coef * offset;
      }

      bilinterm->coef *= coef;
   }

   /* release old variable */
   SCIP_CALL( SCIPreleaseVar(scip, &quadvarterm->var) );

   /* set new variable */
   quadvarterm->var = var;

   /* capture new variable */
   SCIP_CALL( SCIPcaptureVar(scip, quadvarterm->var) );

   /* catch variable events, if we do so */
   if( eventhdlr != NULL )
   {
      /* catch bound change events of variable */
      SCIP_CALL( catchQuadVarEvents(scip, eventhdlr, cons, pos) );
   }

   /* invalidate activity information */
   consdata->activity = SCIP_INVALID;
   SCIPintervalSetEmpty(&consdata->quadactivitybounds);

   /* invalidate nonlinear row */
   if( consdata->nlrow != NULL )
   {
      SCIP_CALL( SCIPreleaseNlRow(scip, &consdata->nlrow) );
   }

   /* install rounding locks for new variable */
   SCIP_CALL( lockQuadraticVariable(scip, cons, var) );

   consdata->isremovedfixings = consdata->isremovedfixings && SCIPvarIsActive(var);
   consdata->quadvarssorted = (consdata->nquadvars == 1);
   consdata->quadvarsmerged = FALSE;
   consdata->bilinsorted &= (quadvarterm->nadjbilin == 0);  /*lint !e514*/
   consdata->bilinmerged &= (quadvarterm->nadjbilin == 0);  /*lint !e514*/

   consdata->ispropagated  = FALSE;
   consdata->ispresolved   = FALSE;
   consdata->iscurvchecked = FALSE;

   return SCIP_OKAY;
}

/** adds a bilinear term to quadratic constraint */
static
SCIP_RETCODE addBilinearTerm(
   SCIP*                 scip,               /**< SCIP data structure */
   SCIP_CONS*            cons,               /**< quadratic constraint */
   int                   var1pos,            /**< position of first variable in quadratic variables array */
   int                   var2pos,            /**< position of second variable in quadratic variables array */
   SCIP_Real             coef                /**< coefficient of bilinear term */
   )
{
   SCIP_CONSDATA* consdata;
   SCIP_BILINTERM* bilinterm;

   assert(scip != NULL);
   assert(cons != NULL);

   if( var1pos == var2pos )
   {
      SCIPerrorMessage("tried to add bilinear term where both variables are the same\n");
      return SCIP_INVALIDDATA;
   }

   consdata = SCIPconsGetData(cons);
   assert(consdata != NULL);

   assert(var1pos >= 0);
   assert(var1pos < consdata->nquadvars);
   assert(var2pos >= 0);
   assert(var2pos < consdata->nquadvars);

   SCIP_CALL( consdataEnsureBilinSize(scip, consdata, consdata->nbilinterms + 1) );

   bilinterm = &consdata->bilinterms[consdata->nbilinterms];
   if( SCIPvarCompare(consdata->quadvarterms[var1pos].var, consdata->quadvarterms[var2pos].var) < 0 )
   {
      bilinterm->var1 = consdata->quadvarterms[var1pos].var;
      bilinterm->var2 = consdata->quadvarterms[var2pos].var;
   }
   else
   {
      bilinterm->var1 = consdata->quadvarterms[var2pos].var;
      bilinterm->var2 = consdata->quadvarterms[var1pos].var;
   }
   bilinterm->coef = coef;

   if( bilinterm->var1 == bilinterm->var2 )
   {
      SCIPerrorMessage("tried to add bilinear term where both variables are the same, but appear at different positions in quadvarterms array\n");
      return SCIP_INVALIDDATA;
   }
   assert(SCIPvarCompare(bilinterm->var1, bilinterm->var2) == -1);

   SCIP_CALL( consdataEnsureAdjBilinSize(scip, &consdata->quadvarterms[var1pos], consdata->quadvarterms[var1pos].nadjbilin + 1) );
   SCIP_CALL( consdataEnsureAdjBilinSize(scip, &consdata->quadvarterms[var2pos], consdata->quadvarterms[var2pos].nadjbilin + 1) );

   consdata->quadvarterms[var1pos].adjbilin[consdata->quadvarterms[var1pos].nadjbilin] = consdata->nbilinterms;
   consdata->quadvarterms[var2pos].adjbilin[consdata->quadvarterms[var2pos].nadjbilin] = consdata->nbilinterms;
   ++consdata->quadvarterms[var1pos].nadjbilin;
   ++consdata->quadvarterms[var2pos].nadjbilin;

   ++consdata->nbilinterms;

   /* invalidate activity information */
   consdata->activity = SCIP_INVALID;
   SCIPintervalSetEmpty(&consdata->quadactivitybounds);

   /* invalidate nonlinear row */
   if( consdata->nlrow != NULL )
   {
      SCIP_CALL( SCIPreleaseNlRow(scip, &consdata->nlrow) );
   }

   consdata->ispropagated = FALSE;
   consdata->ispresolved  = FALSE;
   if( consdata->nbilinterms == 1 )
   {
      consdata->bilinsorted = TRUE;
      consdata->bilinmerged = TRUE;
   }
   else
   {
      consdata->bilinsorted = consdata->bilinsorted
         && (bilinTermComp(consdata, consdata->nbilinterms-2, consdata->nbilinterms-1) >= 0);
      consdata->bilinmerged = FALSE;
   }

   consdata->iscurvchecked = FALSE;

   return SCIP_OKAY;
}

/** removes a set of bilinear terms and updates adjacency information in quad var terms
 * Note: this function sorts the given array termposs */
static
SCIP_RETCODE removeBilinearTermsPos(
   SCIP*                 scip,               /**< SCIP data structure */
   SCIP_CONS*            cons,               /**< quadratic constraint */
   int                   nterms,             /**< number of terms to delete */
   int*                  termposs            /**< indices of terms to delete */
   )
{
   SCIP_CONSDATA* consdata;
   int* newpos;
   int i;
   int j;
   int offset;

   assert(scip != NULL);
   assert(cons != NULL);
   assert(nterms == 0 || termposs != NULL);

   if( nterms == 0 )
      return SCIP_OKAY;

   consdata = SCIPconsGetData(cons);
   assert(consdata != NULL);

   SCIPsortInt(termposs, nterms);

   SCIP_CALL( SCIPallocBufferArray(scip, &newpos, consdata->nbilinterms) );

   i = 0;
   offset = 0;
   for( j = 0; j < consdata->nbilinterms; ++j )
   {
      /* if j'th term is deleted, increase offset and continue */
      if( i < nterms && j == termposs[i] )
      {
         ++offset;
         ++i;
         newpos[j] = -1;
         continue;
      }

      /* otherwise, move it forward and remember new position */
      if( offset > 0 )
         consdata->bilinterms[j-offset] = consdata->bilinterms[j];
      newpos[j] = j - offset;
   }
   assert(offset == nterms);

   /* update adjacency and activity information in quad var terms */
   for( i = 0; i < consdata->nquadvars; ++i )
   {
      offset = 0;
      for( j = 0; j < consdata->quadvarterms[i].nadjbilin; ++j )
      {
         assert(consdata->quadvarterms[i].adjbilin[j] < consdata->nbilinterms);
         if( newpos[consdata->quadvarterms[i].adjbilin[j]] == -1 )
         {
            /* corresponding bilinear term was deleted, thus increase offset */
            ++offset;
         }
         else
         {
            /* update index of j'th bilinear term and store at position j-offset */
            consdata->quadvarterms[i].adjbilin[j-offset] = newpos[consdata->quadvarterms[i].adjbilin[j]];
         }
      }
      consdata->quadvarterms[i].nadjbilin -= offset;
      /* some bilinear term was removed, so invalidate activity bounds */
   }

   consdata->nbilinterms -= nterms;

   SCIPfreeBufferArray(scip, &newpos);

   /* some quad vars may be linear now */
   consdata->quadvarsmerged = FALSE;

   consdata->ispropagated  = FALSE;
   consdata->ispresolved   = FALSE;
   consdata->iscurvchecked = FALSE;

   /* invalidate activity */
   consdata->activity = SCIP_INVALID;
   SCIPintervalSetEmpty(&consdata->quadactivitybounds);

   /* invalidate nonlinear row */
   if( consdata->nlrow != NULL )
   {
      SCIP_CALL( SCIPreleaseNlRow(scip, &consdata->nlrow) );
   }

   return SCIP_OKAY;
}

/* merges quad var terms that correspond to the same variable and does additional cleanup
 * if a quadratic variable terms is actually linear, makes a linear term out of it
 * also replaces squares of binary variables by the binary variables, i.e., adds sqrcoef to lincoef
 */
static
SCIP_RETCODE mergeAndCleanQuadVarTerms(
   SCIP*                 scip,               /**< SCIP data structure */
   SCIP_CONS*            cons                /**< quadratic constraint */
   )
{
   SCIP_QUADVARTERM* quadvarterm;
   SCIP_CONSDATA* consdata;
   int i;
   int j;

   assert(scip != NULL);
   assert(cons != NULL);

   consdata = SCIPconsGetData(cons);

   if( consdata->quadvarsmerged )
      return SCIP_OKAY;

   if( consdata->nquadvars == 0 )
   {
      consdata->quadvarsmerged = TRUE;
      return SCIP_OKAY;
   }

   i = 0;
   while( i < consdata->nquadvars )
   {
      /* make sure quad var terms are sorted (do this in every round, since we may move variables around) */
      SCIP_CALL( consdataSortQuadVarTerms(scip, consdata) );

      quadvarterm = &consdata->quadvarterms[i];

      for( j = i+1; j < consdata->nquadvars && consdata->quadvarterms[j].var == quadvarterm->var; ++j )
      {
         /* add quad var term j to current term i */
         quadvarterm->lincoef += consdata->quadvarterms[j].lincoef;
         quadvarterm->sqrcoef += consdata->quadvarterms[j].sqrcoef;
         if( consdata->quadvarterms[j].nadjbilin > 0 )
         {
            /* move adjacency information from j to i */
            SCIP_CALL( consdataEnsureAdjBilinSize(scip, quadvarterm, quadvarterm->nadjbilin + consdata->quadvarterms[j].nadjbilin) );
            BMScopyMemoryArray(&quadvarterm->adjbilin[quadvarterm->nadjbilin], consdata->quadvarterms[j].adjbilin, consdata->quadvarterms[j].nadjbilin);  /*lint !e866*/
            quadvarterm->nadjbilin += consdata->quadvarterms[j].nadjbilin;
            consdata->quadvarterms[j].nadjbilin = 0;
         }
         consdata->quadvarterms[j].lincoef = 0.0;
         consdata->quadvarterms[j].sqrcoef = 0.0;
         /* mark that activity information in quadvarterm is not up to date anymore */
      }

      /* remove quad var terms i+1..j-1 backwards */
      for( j = j-1; j > i; --j )
      {
         SCIP_CALL( delQuadVarTermPos(scip, cons, j) );
      }

      /* for binary variables, x^2 = x
       * however, we may destroy convexity of a quadratic term that involves also bilinear terms
       * thus, we do this step only if the variable does not appear in any bilinear term */
      if( quadvarterm->sqrcoef != 0.0 && SCIPvarIsBinary(quadvarterm->var) && quadvarterm->nadjbilin == 0 )
      {
         SCIPdebugMessage("replace square of binary variable by itself: <%s>^2 --> <%s>\n", SCIPvarGetName(quadvarterm->var), SCIPvarGetName(quadvarterm->var));
         quadvarterm->lincoef += quadvarterm->sqrcoef;
         quadvarterm->sqrcoef = 0.0;

         /* invalidate nonlinear row */
         if( consdata->nlrow != NULL )
         {
            SCIP_CALL( SCIPreleaseNlRow(scip, &consdata->nlrow) );
         }
      }

      /* if its 0.0 or linear, get rid of it */
      if( SCIPisZero(scip, quadvarterm->sqrcoef) && quadvarterm->nadjbilin == 0 )
      {
         if( !SCIPisZero(scip, quadvarterm->lincoef) )
         {
            /* seem to be a linear term now, thus add as linear term */
            SCIP_CALL( addLinearCoef(scip, cons, quadvarterm->var, quadvarterm->lincoef) );
         }
         /* remove term at pos i */
         SCIP_CALL( delQuadVarTermPos(scip, cons, i) );
      }
      else
      {
         ++i;
      }
   }

   consdata->quadvarsmerged = TRUE;
   SCIPintervalSetEmpty(&consdata->quadactivitybounds);

   return SCIP_OKAY;
}

/* merges entries with same linear variable into one entry and cleans up entries with coefficient 0.0 */
static
SCIP_RETCODE mergeAndCleanLinearVars(
   SCIP*                 scip,               /**< SCIP data structure */
   SCIP_CONS*            cons                /**< quadratic constraint */
   )
{
   SCIP_CONSDATA* consdata;
   SCIP_Real newcoef;
   int i;
   int j;
   int qvarpos;

   assert(scip != NULL);
   assert(cons != NULL);

   consdata = SCIPconsGetData(cons);

   if( consdata->linvarsmerged )
      return SCIP_OKAY;

   if( consdata->nlinvars == 0 )
   {
      consdata->linvarsmerged = TRUE;
      return SCIP_OKAY;
   }

   i = 0;
   while( i < consdata->nlinvars )
   {
      /* make sure linear variables are sorted (do this in every round, since we may move variables around) */
      consdataSortLinearVars(consdata);

      /* sum up coefficients that correspond to variable i */
      newcoef = consdata->lincoefs[i];
      for( j = i+1; j < consdata->nlinvars && consdata->linvars[i] == consdata->linvars[j]; ++j )
         newcoef += consdata->lincoefs[j];
      /* delete the additional variables in backward order */ 
      for( j = j-1; j > i; --j )
      {
         SCIP_CALL( delLinearCoefPos(scip, cons, j) );
      }

      /* check if there is already a quadratic variable term with this variable */
      SCIP_CALL( consdataFindQuadVarTerm(scip, consdata, consdata->linvars[i], &qvarpos) );
      if( qvarpos >= 0)
      {
         /* add newcoef to linear coefficient of quadratic variable and mark linear variable as to delete */
         assert(qvarpos < consdata->nquadvars);
         assert(consdata->quadvarterms[qvarpos].var == consdata->linvars[i]);
         consdata->quadvarterms[qvarpos].lincoef += newcoef;
         newcoef = 0.0;
         SCIPintervalSetEmpty(&consdata->quadactivitybounds);
      }

      /* delete also entry at position i, if it became zero (or was zero before) */
      if( SCIPisZero(scip, newcoef) )
      {
         SCIP_CALL( delLinearCoefPos(scip, cons, i) );
      }
      else
      {
         SCIP_CALL( chgLinearCoefPos(scip, cons, i, newcoef) );
         ++i;
      }
   }

   consdata->linvarsmerged = TRUE;

   return SCIP_OKAY;
}

/* merges bilinear terms with same variables into a single term, removes bilinear terms with coefficient 0.0 */
static
SCIP_RETCODE mergeAndCleanBilinearTerms(
   SCIP*                 scip,               /**< SCIP data structure */
   SCIP_CONS*            cons                /**< quadratic constraint */
   )
{
   SCIP_CONSDATA* consdata;
   SCIP_BILINTERM* bilinterm;
   int i;
   int j;
   int* todelete;
   int ntodelete;

   assert(scip != NULL);
   assert(cons != NULL);

   consdata = SCIPconsGetData(cons);

   if( consdata->bilinmerged )
      return SCIP_OKAY;

   if( consdata->nbilinterms == 0 )
   {
      consdata->bilinmerged = TRUE;
      return SCIP_OKAY;
   }

   /* alloc memory for array of terms that need to be deleted finally */
   ntodelete = 0;
   SCIP_CALL( SCIPallocBufferArray(scip, &todelete, consdata->nbilinterms) );

   /* make sure bilinear terms are sorted */
   SCIP_CALL( consdataSortBilinTerms(scip, consdata) );

   i = 0;
   while( i < consdata->nbilinterms )
   {
      bilinterm = &consdata->bilinterms[i];

      /* sum up coefficients that correspond to same variables as term i */
      for( j = i+1; j < consdata->nbilinterms && bilinterm->var1 == consdata->bilinterms[j].var1 && bilinterm->var2 == consdata->bilinterms[j].var2; ++j )
      {
         bilinterm->coef += consdata->bilinterms[j].coef;
         todelete[ntodelete++] = j;
      }

      /* delete also entry at position i, if it became zero (or was zero before) */
      if( SCIPisZero(scip, bilinterm->coef) )
      {
         todelete[ntodelete++] = i;
      }

      /* continue with term after the current series */
      i = j;
   }

   /* delete bilinear terms */
   SCIP_CALL( removeBilinearTermsPos(scip, cons, ntodelete, todelete) );

   SCIPfreeBufferArray(scip, &todelete);

   consdata->bilinmerged = TRUE;

   return SCIP_OKAY;
}

/** removes fixes (or aggregated) variables from a quadratic constraint */
static
SCIP_RETCODE removeFixedVariables(
   SCIP*                 scip,               /**< SCIP data structure */
   SCIP_CONS*            cons                /**< quadratic constraint */
   )
{
   SCIP_CONSDATA* consdata;
   SCIP_BILINTERM* bilinterm;
   SCIP_Real coef;
   SCIP_Real offset;
   SCIP_VAR* var;
   SCIP_VAR* var2;
   int var2pos;
   int i;
   int j;
   int k;

   SCIP_Bool have_change;

   assert(scip != NULL);
   assert(cons != NULL);

   consdata = SCIPconsGetData(cons);

   have_change = FALSE;
   i = 0;
   while( i < consdata->nlinvars )
   {
      var = consdata->linvars[i];

      if( SCIPvarIsActive(var) )
      {
         ++i;
         continue;
      }

      have_change = TRUE;

      coef = consdata->lincoefs[i];
      offset = 0.0;

      SCIP_CALL( SCIPgetProbvarSum(scip, &var, &coef, &offset) );

      SCIPdebugMessage("  linear term %g*<%s> is replaced by %g * <%s> + %g\n", consdata->lincoefs[i], SCIPvarGetName(consdata->linvars[i]), coef, SCIPvarGetName(var), offset);

      /* delete previous variable (this will move another variable to position i) */
      SCIP_CALL( delLinearCoefPos(scip, cons, i) );

      /* put constant part into bounds */
      if( offset != 0.0 )
      {
         if( !SCIPisInfinity(scip, -consdata->lhs) )
            consdata->lhs -= offset;
         if( !SCIPisInfinity(scip,  consdata->rhs) )
            consdata->rhs -= offset;
      }

      /* nothing left to do if variable had been fixed */
      if( coef == 0.0 )
         continue;

      /* if GetProbvar gave a linear variable, just add it
       * if it's a multilinear variable, add it's disaggregated variables */
      if( SCIPvarIsActive(var) )
      {
         SCIP_CALL( addLinearCoef(scip, cons, var, coef) );
      }
      else
      {
         int        naggrs;
         SCIP_VAR** aggrvars;
         SCIP_Real* aggrscalars;
         SCIP_Real  aggrconstant;

         assert(SCIPvarGetStatus(var) == SCIP_VARSTATUS_MULTAGGR);

         naggrs = SCIPvarGetMultaggrNVars(var);
         aggrvars = SCIPvarGetMultaggrVars(var);
         aggrscalars = SCIPvarGetMultaggrScalars(var);
         aggrconstant = SCIPvarGetMultaggrConstant(var);

         SCIP_CALL( consdataEnsureLinearVarsSize(scip, consdata, consdata->nlinvars + naggrs) );

         for( j = 0; j < naggrs; ++j )
         {
            SCIP_CALL( addLinearCoef(scip, cons, aggrvars[j], coef * aggrscalars[j]) );
         }

         if( aggrconstant != 0.0 )
         {
            if( !SCIPisInfinity(scip, -consdata->lhs) )
               consdata->lhs -= coef * aggrconstant;
            if( !SCIPisInfinity(scip,  consdata->rhs) )
               consdata->rhs -= coef * aggrconstant;
         }
      }
   }

   i = 0;
   while( i < consdata->nquadvars )
   {
      var = consdata->quadvarterms[i].var;

      if( SCIPvarIsActive(var) )
      {
         ++i;
         continue;
      }

      have_change = TRUE;

      coef   = 1.0;
      offset = 0.0;
      SCIP_CALL( SCIPgetProbvarSum(scip, &var, &coef, &offset) );

      SCIPdebugMessage("  quadratic variable <%s> with status %d is replaced by %g * <%s> + %g\n", SCIPvarGetName(consdata->quadvarterms[i].var), SCIPvarGetStatus(consdata->quadvarterms[i].var), coef, SCIPvarGetName(var), offset);

      /* handle fixed variable */
      if( coef == 0.0 )
      {
         /* if not fixed to 0.0, add to linear coefs of vars in bilinear terms, and deal with linear and square term as constant */ 
         if( offset != 0.0 )
         {
            for( j = 0; j < consdata->quadvarterms[i].nadjbilin; ++j )
            {
               bilinterm = &consdata->bilinterms[consdata->quadvarterms[i].adjbilin[j]];

               var2 = bilinterm->var1 == consdata->quadvarterms[i].var ? bilinterm->var2 : bilinterm->var1;
               assert(var2 != consdata->quadvarterms[i].var);

               var2pos = 0;
               while( consdata->quadvarterms[var2pos].var != var2 )
               {
                  ++var2pos;
                  assert(var2pos < consdata->nquadvars);
               }
               consdata->quadvarterms[var2pos].lincoef += bilinterm->coef * offset;
            }

            offset = consdata->quadvarterms[i].lincoef * offset + consdata->quadvarterms[i].sqrcoef * offset * offset;
            if( !SCIPisInfinity(scip, -consdata->lhs) )
               consdata->lhs -= offset;
            if( !SCIPisInfinity(scip,  consdata->rhs) )
               consdata->rhs -= offset;
         }

         /* remove bilinear terms */
         SCIP_CALL( removeBilinearTermsPos(scip, cons, consdata->quadvarterms[i].nadjbilin, consdata->quadvarterms[i].adjbilin) );

         /* delete quad. var term i */
         SCIP_CALL( delQuadVarTermPos(scip, cons, i) );

         continue;
      }

      assert(var != NULL);

      /* if GetProbvar gave an active variable, replace the quad var term so that it uses the new variable */
      if( SCIPvarIsActive(var) )
      {
         /* replace x by coef*y+offset */
         SCIP_CALL( replaceQuadVarTermPos(scip, cons, i, var, coef, offset) );

         continue;
      }
      else
      {
         /* if GetProbVar gave a multi-aggregated variable, add new quad var terms and new bilinear terms
          * x is replaced by coef * (sum_i a_ix_i + b) + offset
          * lcoef * x + scoef * x^2 + bcoef * x * y ->
          *   (b*coef + offset) * (lcoef + (b*coef + offset) * scoef)
          * + sum_i a_i*coef * (lcoef + 2 (b*coef + offset) * scoef) x_i
          * + sum_i (a_i*coef)^2 * scoef * x_i^2
          * + 2 sum_{i,j, i<j} (a_i a_j coef^2 scoef) x_i x_j
          * + bcoef * (b*coef + offset + coef * sum_i a_ix_i) y 
          */
         int        naggrs;
         SCIP_VAR** aggrvars;     /* x_i */
         SCIP_Real* aggrscalars;  /* a_i */
         SCIP_Real  aggrconstant; /* b */
         int nquadtermsold;

         SCIP_Real lcoef;
         SCIP_Real scoef;

         assert(SCIPvarGetStatus(var) == SCIP_VARSTATUS_MULTAGGR);

         naggrs = SCIPvarGetMultaggrNVars(var);
         aggrvars = SCIPvarGetMultaggrVars(var);
         aggrscalars = SCIPvarGetMultaggrScalars(var);
         aggrconstant = SCIPvarGetMultaggrConstant(var);

         lcoef = consdata->quadvarterms[i].lincoef;
         scoef = consdata->quadvarterms[i].sqrcoef;

         nquadtermsold = consdata->nquadvars;

         SCIP_CALL( consdataEnsureQuadVarTermsSize(scip, consdata, consdata->nquadvars + naggrs) );

         /* take care of constant part */
         if( aggrconstant != 0.0 || offset != 0.0 )
         {
            SCIP_Real constant;
            constant = (aggrconstant * coef + offset) * (lcoef + (aggrconstant * coef + offset) * scoef);
            if( !SCIPisInfinity(scip, -consdata->lhs) )
               consdata->lhs -= constant;
            if( !SCIPisInfinity(scip,  consdata->rhs) )
               consdata->rhs -= constant;
         }

         /* add x_i's with linear and square coefficients */
         for( j = 0; j < naggrs; ++j )
         {
            SCIP_CALL( addQuadVarTerm(scip, cons, aggrvars[j],
                  coef * aggrscalars[j] * (lcoef + 2.0 * scoef * (coef * aggrconstant + offset)),
                  coef * coef * aggrscalars[j] * aggrscalars[j] * scoef,
                  TRUE) );
         }

         /* ensure space for bilinear terms */
         SCIP_CALL( consdataEnsureBilinSize(scip, consdata, consdata->nquadvars + (scoef != 0.0 ? (naggrs * (naggrs-1))/2 : 0) + consdata->quadvarterms[j].nadjbilin * naggrs) );

         /* add x_j*x_k's */
         if( scoef != 0.0 )
         {
            for( j = 0; j < naggrs; ++j )
               for( k = 0; k < j; ++k )
               {
                  assert(aggrvars[j] != aggrvars[k]);
                  SCIP_CALL( addBilinearTerm(scip, cons, nquadtermsold + j, nquadtermsold + k, 
                        2.0 * aggrscalars[j] * aggrscalars[k] * coef * coef * scoef) );
               }
         }

         /* add x_i*y's */
         for( k = 0; k < consdata->quadvarterms[i].nadjbilin; ++k )
         {
            bilinterm = &consdata->bilinterms[consdata->quadvarterms[i].adjbilin[k]];
            var2 = (bilinterm->var1 == consdata->quadvarterms[i].var) ? bilinterm->var2 : bilinterm->var1;
            assert(var2 != consdata->quadvarterms[i].var);

            /* this is not efficient, but we cannot sort the quadratic terms here, since we currently iterate over them */
            var2pos = 0;
            while( consdata->quadvarterms[var2pos].var != var2 )
            {
               ++var2pos;
               assert(var2pos < consdata->nquadvars);
            }

            for( j = 0; j < naggrs; ++j )
            {
               if( aggrvars[j] == var2 )
               { /* x_i == y, so we have a square term here */
                  consdata->quadvarterms[var2pos].sqrcoef += bilinterm->coef * coef * aggrscalars[j];
               }
               else
               { /* x_i != y, so we need to add a bilinear term here */
                  SCIP_CALL( addBilinearTerm(scip, cons, nquadtermsold + j, var2pos,
                        bilinterm->coef * coef * aggrscalars[j]) );
               }
            }

            consdata->quadvarterms[var2pos].lincoef += bilinterm->coef * (aggrconstant * coef + offset);
         }

         /* remove bilinear terms */
         SCIP_CALL( removeBilinearTermsPos(scip, cons, consdata->quadvarterms[i].nadjbilin, consdata->quadvarterms[i].adjbilin) );

         /* delete quad. var term i */
         SCIP_CALL( delQuadVarTermPos(scip, cons, i) );
      }
   }

   consdata->isremovedfixings = TRUE;

   SCIPdebugMessage("removed fixations from <%s>\n  -> ", SCIPconsGetName(cons));
   SCIPdebugPrintCons(scip, cons, NULL);

#ifndef NDEBUG
   for( i = 0; i < consdata->nlinvars; ++i )
      assert(SCIPvarIsActive(consdata->linvars[i]));

   for( i = 0; i < consdata->nquadvars; ++i )
      assert(SCIPvarIsActive(consdata->quadvarterms[i].var));
#endif

   if( !have_change )
      return SCIP_OKAY;

   /* some quadratic variable may have been replaced by an already existing linear variable
    * in this case, we want the linear variable to be removed, which happens in mergeAndCleanLinearVars
    */ 
   consdata->linvarsmerged = FALSE;

   SCIP_CALL( mergeAndCleanBilinearTerms(scip, cons) );
   SCIP_CALL( mergeAndCleanQuadVarTerms(scip, cons) );
   SCIP_CALL( mergeAndCleanLinearVars(scip, cons) );

#ifndef NDEBUG
   for( i = 0; i < consdata->nbilinterms; ++i )
   {
      assert(consdata->bilinterms[i].var1 != consdata->bilinterms[i].var2);
      assert(consdata->bilinterms[i].coef != 0.0);
      assert(SCIPvarCompare(consdata->bilinterms[i].var1, consdata->bilinterms[i].var2) < 0);
   }
#endif

   return SCIP_OKAY;
}

/** create a nonlinear row representation of the constraint and stores them in consdata */
static
SCIP_RETCODE createNlRow(
   SCIP*                 scip,               /**< SCIP data structure */
   SCIP_CONS*            cons                /**< quadratic constraint */
   )
{
   SCIP_CONSDATA* consdata;
   int        nquadvars;     /* number of variables in quadratic terms */
   SCIP_VAR** quadvars;      /* variables in quadratic terms */
   int        nquadelems;    /* number of quadratic elements (square and bilinear terms) */
   SCIP_QUADELEM* quadelems; /* quadratic elements (square and bilinear terms) */
   int        nquadlinterms; /* number of linear terms using variables that are in quadratic terms */
   SCIP_VAR** quadlinvars;   /* variables of linear terms using variables that are in quadratic terms */
   SCIP_Real* quadlincoefs;  /* coefficients of linear terms using variables that are in quadratic terms */
   int i;
   int idx1;
   int idx2;
   int lincnt;
   int elcnt;
   SCIP_VAR* lastvar;
   int lastvaridx;

   assert(scip != NULL);
   assert(cons != NULL);

   consdata = SCIPconsGetData(cons);
   assert(consdata != NULL);

   if( consdata->nlrow != NULL )
   {
      SCIP_CALL( SCIPreleaseNlRow(scip, &consdata->nlrow) );
   }

   nquadvars = consdata->nquadvars;
   nquadelems = consdata->nbilinterms;
   nquadlinterms = 0;
   for( i = 0; i < nquadvars; ++i )
   {
      if( consdata->quadvarterms[i].sqrcoef != 0.0 )
         ++nquadelems;
      if( !SCIPisZero(scip, consdata->quadvarterms[i].lincoef) )
         ++nquadlinterms;
   }

   SCIP_CALL( SCIPallocBufferArray(scip, &quadvars,  nquadvars) );
   SCIP_CALL( SCIPallocBufferArray(scip, &quadelems, nquadelems) );
   SCIP_CALL( SCIPallocBufferArray(scip, &quadlinvars,  nquadlinterms) );
   SCIP_CALL( SCIPallocBufferArray(scip, &quadlincoefs, nquadlinterms) );

   lincnt = 0;
   elcnt = 0;
   for( i = 0; i < nquadvars; ++i )
   {
      quadvars[i] = consdata->quadvarterms[i].var;

      if( consdata->quadvarterms[i].sqrcoef != 0.0 )
      {
         assert(elcnt < nquadelems);
         quadelems[elcnt].idx1 = i;
         quadelems[elcnt].idx2 = i;
         quadelems[elcnt].coef = consdata->quadvarterms[i].sqrcoef;
         ++elcnt;
      }

      if( !SCIPisZero(scip, consdata->quadvarterms[i].lincoef) )
      {
         assert(lincnt < nquadlinterms);
         quadlinvars [lincnt] = consdata->quadvarterms[i].var;
         quadlincoefs[lincnt] = consdata->quadvarterms[i].lincoef;
         ++lincnt;
      }
   }
   assert(lincnt == nquadlinterms);

   /* bilinear terms are sorted first by first variable, then by second variable
    * thus, it makes sense to remember the index of the previous first variable for the case a series of bilinear terms with the same first var appears */
   lastvar = NULL;
   lastvaridx = -1;
   for( i = 0; i < consdata->nbilinterms; ++i )
   {
      if( lastvar == consdata->bilinterms[i].var1 )
      {
         assert(lastvaridx >= 0);
         assert(consdata->quadvarterms[lastvaridx].var == consdata->bilinterms[i].var1);
      }
      else
      {
         lastvar = consdata->bilinterms[i].var1;
         SCIP_CALL( consdataFindQuadVarTerm(scip, consdata, lastvar, &lastvaridx) );
      }
      idx1 = lastvaridx;

      SCIP_CALL( consdataFindQuadVarTerm(scip, consdata, consdata->bilinterms[i].var2, &idx2) );

      assert(elcnt < nquadelems);
      quadelems[elcnt].idx1 = MIN(idx1, idx2);
      quadelems[elcnt].idx2 = MAX(idx1, idx2);
      quadelems[elcnt].coef = consdata->bilinterms[i].coef;
      ++elcnt;
   }
   assert(elcnt == nquadelems);

   SCIP_CALL( SCIPcreateNlRow(scip, &consdata->nlrow, SCIPconsGetName(cons), 0.0,
         consdata->nlinvars, consdata->linvars, consdata->lincoefs,
         nquadvars, quadvars, nquadelems, quadelems,
         NULL, consdata->lhs, consdata->rhs) );

   SCIP_CALL( SCIPaddLinearCoefsToNlRow(scip, consdata->nlrow, nquadlinterms, quadlinvars, quadlincoefs) );

   SCIPfreeBufferArray(scip, &quadvars);
   SCIPfreeBufferArray(scip, &quadelems);
   SCIPfreeBufferArray(scip, &quadlinvars);
   SCIPfreeBufferArray(scip, &quadlincoefs);

   return SCIP_OKAY;
}

static
SCIP_RETCODE presolveSolve(
   SCIP*                 scip,               /**< SCIP data structure */
   SCIP_CONS*            cons,               /**< constraint */
   SCIP_RESULT*          result,             /**< to store result of solve: cutoff, success, or do-not-find */
   SCIP_Bool*            redundant,          /**< to store whether constraint is redundant now (should be deleted) */
   int*                  naggrvars           /**< counter on number of variable aggregations */
   )
{
   SCIP_CONSDATA* consdata;

   assert(scip != NULL);
   assert(cons != NULL);
   assert(result != NULL);
   assert(redundant != NULL);

   *result = SCIP_DIDNOTFIND;
   *redundant = FALSE;

   consdata = SCIPconsGetData(cons);
   assert(consdata != NULL);

   /* if constraint is an equality with two variables, at least one of them binary,
    * and linear after fixing the binary, then we can aggregate the variables */
   if( SCIPisEQ(scip, consdata->lhs, consdata->rhs) && consdata->nlinvars == 0 && consdata->nquadvars == 2 &&
      ((SCIPvarIsBinary(consdata->quadvarterms[0].var) && consdata->quadvarterms[1].sqrcoef == 0.0) ||
       (SCIPvarIsBinary(consdata->quadvarterms[1].var) && consdata->quadvarterms[0].sqrcoef == 0.0)) )
   {
      SCIP_Bool infeasible;
      SCIP_Bool aggregated;
      SCIP_Real a;
      SCIP_Real b;
      SCIP_Real c;
      SCIP_VAR* x;
      SCIP_VAR* y;
      int binvaridx;

      /* constraint is a*(x+x^2) + b*y + c*x*y = rhs, with x binary variable
       * x = 0 -> b*y == rhs
       * x = 1 -> (b+c)*y == rhs - a
       *
       * if b != 0 and b+c != 0, then y = (rhs-a)/(b+c) * x + rhs/b * (1-x) = ((rhs-a)/(b+c) - rhs/b) * x + rhs/b
       */

      binvaridx = (SCIPvarIsBinary(consdata->quadvarterms[0].var) && consdata->quadvarterms[1].sqrcoef == 0.0) ? 0 : 1;

      x = consdata->quadvarterms[binvaridx].var;
      a = consdata->quadvarterms[binvaridx].sqrcoef + consdata->quadvarterms[binvaridx].lincoef;

      y = consdata->quadvarterms[1-binvaridx].var;
      b = consdata->quadvarterms[1-binvaridx].lincoef;

      assert(consdata->nbilinterms <= 1);  /* should actually be 1, since constraint is otherwise linear */
      c = (consdata->nbilinterms == 1) ? consdata->bilinterms[0].coef : 0.0;

      if( !SCIPisZero(scip, b) && !SCIPisZero(scip, b+c) )
      {
         SCIPdebugMessage("<%s> = 0 -> %g*<%s> = %g  and  <%s> = 1 -> %g*<%s> = %g\n", SCIPvarGetName(x), b, SCIPvarGetName(y), consdata->rhs, SCIPvarGetName(x), b+c, SCIPvarGetName(y), consdata->rhs - a);
         SCIPdebugMessage("=> attempt aggregation <%s> = %g*<%s> + %g\n", SCIPvarGetName(y), (consdata->rhs-a)/(b+c) - consdata->rhs/b, SCIPvarGetName(x), consdata->rhs/b);

         SCIP_CALL( SCIPaggregateVars(scip, x, y, (consdata->rhs-a)/(b+c) - consdata->rhs/b, -1.0, -consdata->rhs/b, &infeasible, redundant, &aggregated) );
         if( infeasible )
            *result = SCIP_CUTOFF;
         else if( *redundant || aggregated )
         {
            /* aggregated (or were already aggregated), so constraint is now redundant */
            *result = SCIP_SUCCESS;
            *redundant = TRUE;

            if( aggregated )
               ++*naggrvars;
         }
      }

      /* @todo if b is 0 or b+c is 0, or lhs != rhs, then could replace by varbound constraint */
   }

   return SCIP_OKAY;
}


/** reformulates products of binary variables as AND constraint
 *  For a product x*y, with x and y binary variables, the product is replaced by a new auxiliary variable z and the constraint z = {x and y} is added.
 */
static
SCIP_RETCODE presolveTryAddAND(
   SCIP*                 scip,               /**< SCIP data structure */
   SCIP_CONSHDLR*        conshdlr,           /**< constraint handler */
   SCIP_CONS*            cons,               /**< constraint */
   int*                  naddconss           /**< buffer where to add the number of AND constraints added */
   )
{
   SCIP_CONSHDLRDATA* conshdlrdata;
   SCIP_CONSDATA*     consdata;
   char               name[SCIP_MAXSTRLEN];
   SCIP_VAR*          vars[2];
   SCIP_VAR*          auxvar;
   SCIP_CONS*         andcons;
   int                i;
   int                ntodelete;
   int*               todelete;

   assert(scip != NULL);
   assert(conshdlr != NULL);
   assert(cons != NULL);
   assert(naddconss != NULL);

   conshdlrdata = SCIPconshdlrGetData(conshdlr);
   assert(conshdlrdata != NULL);

   /* if user does not like AND very much, then return */
   if( conshdlrdata->empathy4and < 2 )
      return SCIP_OKAY;

   consdata = SCIPconsGetData(cons);
   assert(consdata != NULL);

   if( consdata->nbilinterms == 0 )
      return SCIP_OKAY;

   /* get array to store indices of bilinear terms that shall be deleted */
   SCIP_CALL( SCIPallocBufferArray(scip, &todelete, consdata->nbilinterms) );
   ntodelete = 0;

   for( i = 0; i < consdata->nbilinterms; ++i )
   {
      vars[0] = consdata->bilinterms[i].var1;
      if( !SCIPvarIsBinary(vars[0]) )
         continue;

      vars[1] = consdata->bilinterms[i].var2;
      if( !SCIPvarIsBinary(vars[1]) )
         continue;

      /* create auxiliary variable */ 
      (void)SCIPsnprintf(name, SCIP_MAXSTRLEN, "prod%s_%s_%s", SCIPvarGetName(vars[0]), SCIPvarGetName(vars[1]), SCIPconsGetName(cons));
      SCIP_CALL( SCIPcreateVar(scip, &auxvar, name, 0.0, 1.0, 0.0, SCIP_VARTYPE_BINARY, 
            SCIPvarIsInitial(vars[0]) || SCIPvarIsInitial(vars[1]), SCIPvarIsRemovable(vars[0]) && SCIPvarIsRemovable(vars[1]), NULL, NULL, NULL, NULL, NULL) );
      SCIP_CALL( SCIPaddVar(scip, auxvar) );
#ifdef SCIP_DEBUG_SOLUTION
      if( SCIPdebugIsMainscip(scip) )
      {
         SCIP_Real var0val;
         SCIP_Real var1val;
         SCIP_CALL( SCIPdebugGetSolVal(scip, vars[0], &var0val) );
         SCIP_CALL( SCIPdebugGetSolVal(scip, vars[1], &var1val) );
         SCIP_CALL( SCIPdebugAddSolVal(scip, auxvar, var0val * var1val) );
      }
#endif

      /* create and constraint auxvar = x and y */
      (void)SCIPsnprintf(name, SCIP_MAXSTRLEN, "%sAND%s", SCIPvarGetName(vars[0]), SCIPvarGetName(vars[1]));
      SCIP_CALL( SCIPcreateConsAnd(scip, &andcons, name, auxvar, 2, vars,
            SCIPconsIsInitial(cons) && conshdlrdata->binreforminitial,
            SCIPconsIsSeparated(cons), SCIPconsIsEnforced(cons), SCIPconsIsChecked(cons),
            SCIPconsIsPropagated(cons),  SCIPconsIsLocal(cons), SCIPconsIsModifiable(cons),
            SCIPconsIsDynamic(cons), SCIPconsIsRemovable(cons), SCIPconsIsStickingAtNode(cons)) );
      SCIP_CALL( SCIPaddCons(scip, andcons) );
      SCIPdebugMessage("added AND constraint: ");
      SCIPdebugPrintCons(scip, andcons, NULL);
      SCIP_CALL( SCIPreleaseCons(scip, &andcons) );
      ++*naddconss;

      /* add bilincoef * auxvar to linear terms */
      SCIP_CALL( addLinearCoef(scip, cons, auxvar, consdata->bilinterms[i].coef) );
      SCIP_CALL( SCIPreleaseVar(scip, &auxvar) );

      /* remember that we have to delete this bilinear term */
      assert(ntodelete < consdata->nbilinterms);
      todelete[ntodelete++] = i;
   }

   /* remove bilinear terms that have been replaced */
   SCIP_CALL( removeBilinearTermsPos(scip, cons, ntodelete, todelete) );
   SCIPfreeBufferArray(scip, &todelete);

   return SCIP_OKAY;
}

/** gets bounds of variable y if x takes a certain value
 * checks whether x = xval has implications on y
 */
static
void getImpliedBounds(
   SCIP_VAR*             x,                  /**< variable which implications to check */
   SCIP_Bool             xval,               /**< value of x to check for (TRUE for 1, FALSE for 0) */
   SCIP_VAR*             y,                  /**< variable to check if bounds can be reduced */
   SCIP_INTERVAL*        resultant           /**< buffer to store bounds on y */
   )
{
   int nimpls;
   int nbinimpls;
   SCIP_VAR** implvars;
   SCIP_BOUNDTYPE* impltypes;
   SCIP_Real* implbounds;
   int pos;

   assert(x != NULL);
   assert(y != NULL);
   assert(resultant != NULL);

   SCIPintervalSetBounds(resultant, MIN(SCIPvarGetLbGlobal(y), SCIPvarGetUbGlobal(y)), MAX(SCIPvarGetLbGlobal(y), SCIPvarGetUbGlobal(y)));  /*lint !e666 */

   if( !SCIPvarIsBinary(x) || !SCIPvarIsActive(x) )
      return;

   /* analyze implications for x = xval */
   nimpls = SCIPvarGetNImpls(x, xval);
   if( nimpls == 0 )
      return;

   nbinimpls  = SCIPvarGetNBinImpls (x, xval);
   implvars   = SCIPvarGetImplVars  (x, xval);
   impltypes  = SCIPvarGetImplTypes (x, xval);
   implbounds = SCIPvarGetImplBounds(x, xval);

   assert(implvars != NULL);
   assert(impltypes != NULL);
   assert(implbounds != NULL);

   if( SCIPvarGetType(y) == SCIP_VARTYPE_BINARY )
   {
      if( !SCIPsortedvecFindPtr((void**)implvars, SCIPvarComp, (void*)y, nbinimpls, &pos) )
         return;
   }
   else if( nbinimpls < nimpls )
   {
      if( !SCIPsortedvecFindPtr((void**)&implvars[nbinimpls], SCIPvarComp, (void*)y, nimpls - nbinimpls, &pos) )
         return;
   }
   else
      return;

   /* if there are several implications on y, go to the first one */
   while( pos > 0 && implvars[pos-1] == y )
      --pos;

   /* update implied lower and upper bounds on y
    * but make sure that resultant will not be empty, due to tolerances
    */
   while( pos < nimpls && implvars[pos] == y )
   {
      if( impltypes[pos] == SCIP_BOUNDTYPE_LOWER )
         resultant->inf = MAX(resultant->inf, MIN(resultant->sup, implbounds[pos]));
      else
         resultant->sup = MIN(resultant->sup, MAX(resultant->inf, implbounds[pos]));
      ++pos;
   }

   assert(!SCIPintervalIsEmpty(*resultant));
}

/** Reformulates products of binary times bounded continuous variables as system of linear inequalities (plus auxiliary variable).
 * 
 *  For a product x*y, with y a binary variable and x a continous variable with finite bounds,
 *  an auxiliary variable z and the inequalities \f$ x^L * y \leq z \leq x^U * y \f$ and \f$ x - (1-y)*x^U \leq z \leq x - (1-y)*x^L \f$ are added.
 * 
 *  If x is a linear term consisting of more than one variable, it is split up in groups of linear terms of length at most maxnrvar.
 *  For each product of linear term of length at most maxnrvar with y, an auxiliary z and linear inequalities are added.
 * 
 *  If y is a binary variable, the AND constraint \f$ z = x \wedge y \f$ may be added instead of linear constraints.
 */
static
SCIP_RETCODE presolveTryAddLinearReform(
   SCIP*                 scip,               /**< SCIP data structure */
   SCIP_CONSHDLR*        conshdlr,           /**< constraint handler */
   SCIP_CONS*            cons,               /**< constraint */
   int*                  naddconss           /**< buffer where to add the number of auxiliary constraints added */
   )
{  /*lint --e{666} */
   SCIP_CONSHDLRDATA* conshdlrdata;
   SCIP_CONSDATA*     consdata;
   SCIP_VAR**         xvars;
   SCIP_Real*         xcoef;
   SCIP_INTERVAL      xbndszero;
   SCIP_INTERVAL      xbndsone;
   SCIP_INTERVAL      act0;
   SCIP_INTERVAL      act1;
   int                nxvars;
   SCIP_VAR*          y;
   SCIP_VAR*          bvar;
   char               name[SCIP_MAXSTRLEN];
   int                nbilinterms;
   SCIP_VAR*          auxvar;
   SCIP_CONS*         auxcons;
   int                i;
   int                j;
   int                k;
   int                bilinidx;
   SCIP_Real          bilincoef;
   SCIP_Real          mincoef;
   SCIP_Real          maxcoef;
   int*               todelete;
   int                ntodelete;
   int                maxnrvar;
   SCIP_Bool          integral;
   SCIP_Longint       gcd;
   SCIP_Bool          auxvarinitial;
   SCIP_Bool          auxvarremovable;

   assert(scip != NULL);
   assert(conshdlr != NULL);
   assert(cons != NULL);
   assert(naddconss != NULL);

   conshdlrdata = SCIPconshdlrGetData(conshdlr);
   assert(conshdlrdata != NULL);

   maxnrvar = conshdlrdata->replacebinaryprodlength;
   if( maxnrvar == 0 )
      return SCIP_OKAY;

   consdata = SCIPconsGetData(cons);
   assert(consdata != NULL);

   xvars = NULL;
   xcoef = NULL;
   todelete = NULL;
   gcd = 0;

   for( i = 0; i < consdata->nquadvars; ++i )
   {
      y = consdata->quadvarterms[i].var;
      if( !SCIPvarIsBinary(y) )
         continue;

      nbilinterms = consdata->quadvarterms[i].nadjbilin;
      if( nbilinterms == 0 )
         continue;

      SCIP_CALL( SCIPreallocBufferArray(scip, &xvars, MIN(maxnrvar, nbilinterms)+2) ); /* add 2 for later use when creating linear constraints */
      SCIP_CALL( SCIPreallocBufferArray(scip, &xcoef, MIN(maxnrvar, nbilinterms)+2) );

      /* alloc array to store indices of bilinear terms that shall be deleted */
      SCIP_CALL( SCIPreallocBufferArray(scip, &todelete, nbilinterms) );
      ntodelete = 0;

      auxvarinitial = SCIPvarIsInitial(y);
      auxvarremovable = SCIPvarIsRemovable(y);

      /* setup a list of bounded variables x_i with coefficients a_i that are multiplied with binary y: y*(sum_i a_i*x_i)
       * and compute range of sum_i a_i*x_i for the cases y = 0 and y = 1
       * we may need several rounds of maxnrvar < nbilinterms
       */
      j = 0;
      do
      {
         nxvars = 0;
         SCIPintervalSet(&xbndszero, 0.0);
         SCIPintervalSet(&xbndsone, 0.0);

         mincoef = SCIPinfinity(scip);
         maxcoef = 0.0;
         integral = TRUE;

         /* collect at most maxnrvar variables for x term */
         for( ; j < nbilinterms && nxvars < maxnrvar; ++j )
         {
            bilinidx = consdata->quadvarterms[i].adjbilin[j];
            assert(bilinidx >= 0);
            assert(bilinidx < consdata->nbilinterms);

            bvar = consdata->bilinterms[bilinidx].var1;
            if( bvar == y )
               bvar = consdata->bilinterms[bilinidx].var2;
            assert(bvar != y);

            /* skip products with unbounded variables */
            if( SCIPisInfinity(scip, -SCIPvarGetLbGlobal(bvar)) || SCIPisInfinity(scip, SCIPvarGetUbGlobal(bvar)) )
            {
               SCIPdebugMessage("skip reform of <%s><%s> due to unbounded second variable [%g,%g]\n",
                  SCIPvarGetName(y), SCIPvarGetName(bvar), SCIPvarGetLbGlobal(bvar), SCIPvarGetUbGlobal(bvar));
               continue;
            }

            bilincoef = consdata->bilinterms[bilinidx].coef;
            assert(bilincoef != 0.0);

            /* get activity of bilincoef * x if y = 0 */
            getImpliedBounds(y, FALSE, bvar, &act0);
            SCIPintervalMulScalar(SCIPinfinity(scip), &act0, act0, bilincoef);

            /* get activity of bilincoef * x if y = 1 */
            getImpliedBounds(y,  TRUE, bvar, &act1);
            SCIPintervalMulScalar(SCIPinfinity(scip), &act1, act1, bilincoef);

            /* skip products that give rise to very large coefficients (big big-M's) */
            if( SCIPfeastol(scip) * REALABS(act0.inf) >= conshdlrdata->binreformmaxcoef || SCIPfeastol(scip) * REALABS(act0.sup) >= conshdlrdata->binreformmaxcoef )
            {
               SCIPdebugMessage("skip reform of %g<%s><%s> due to huge activity [%g,%g] for <%s> = 0.0\n",
                  bilincoef, SCIPvarGetName(y), SCIPvarGetName(bvar), SCIPintervalGetInf(act0), SCIPintervalGetSup(act0), SCIPvarGetName(y));
               continue;
            }
            if( SCIPfeastol(scip) * REALABS(act1.inf) >= conshdlrdata->binreformmaxcoef || SCIPfeastol(scip) * REALABS(act1.sup) >= conshdlrdata->binreformmaxcoef )
            {
               SCIPdebugMessage("skip reform of %g<%s><%s> due to huge activity [%g,%g] for <%s> = 1.0\n",
                  bilincoef, SCIPvarGetName(y), SCIPvarGetName(bvar), SCIPintervalGetInf(act1), SCIPintervalGetSup(act1), SCIPvarGetName(y));
               continue;
            }
            if( !SCIPisZero(scip, MIN(REALABS(act0.inf), REALABS(act0.sup))) &&
               SCIPfeastol(scip) * MAX(REALABS(act0.inf), REALABS(act0.sup)) / MIN(REALABS(act0.inf), REALABS(act0.sup)) >= conshdlrdata->binreformmaxcoef )
            {
               SCIPdebugMessage("skip reform of %g<%s><%s> due to huge activity ratio %g for <%s> = 0.0\n",
                  bilincoef, SCIPvarGetName(y), SCIPvarGetName(bvar), MAX(REALABS(act0.inf), REALABS(act0.sup)) / MIN(REALABS(act0.inf), REALABS(act0.sup)), SCIPvarGetName(y));
               continue;
            }
            if( !SCIPisZero(scip, MIN(REALABS(act1.inf), REALABS(act1.sup))) &&
               SCIPfeastol(scip) * MAX(REALABS(act1.inf), REALABS(act1.sup)) / MIN(REALABS(act1.inf), REALABS(act1.sup)) >= conshdlrdata->binreformmaxcoef )
            {
               SCIPdebugMessage("skip reform of %g<%s><%s> due to huge activity ratio %g for <%s> = 0.0\n",
                  bilincoef, SCIPvarGetName(y), SCIPvarGetName(bvar), MAX(REALABS(act1.inf), REALABS(act1.sup)) / MIN(REALABS(act1.inf), REALABS(act1.sup)), SCIPvarGetName(y));
               continue;
            }

            /* add bvar to x term */  
            xvars[nxvars] = bvar;
            xcoef[nxvars] = bilincoef;
            ++nxvars;

            /* update bounds on x term */
            SCIPintervalAdd(SCIPinfinity(scip), &xbndszero, xbndszero, act0);
            SCIPintervalAdd(SCIPinfinity(scip), &xbndsone,  xbndsone,  act1);

            if( REALABS(bilincoef) < mincoef )
               mincoef = ABS(bilincoef);
            if( REALABS(bilincoef) > maxcoef )
               maxcoef = ABS(bilincoef);

            /* update whether all coefficients will be integral and if so, compute their gcd */
            integral &= (SCIPvarGetType(bvar) < SCIP_VARTYPE_CONTINUOUS) && SCIPisIntegral(scip, bilincoef);  /*lint !e514 */
            if( integral )
            {
               if( nxvars == 1 )
                  gcd = (SCIP_Longint)SCIPround(scip, REALABS(bilincoef));
               else
                  gcd = SCIPcalcGreComDiv(gcd, (SCIP_Longint)SCIPround(scip, REALABS(bilincoef)));
            }

            /* if bvar is initial, then also the auxiliary variable should be initial
             * if bvar is not removable, then also the auxiliary variable should not be removable
             */
            auxvarinitial |= SCIPvarIsInitial(bvar);
            auxvarremovable &= SCIPvarIsRemovable(bvar);

            /* remember that we have to remove this bilinear term later */
            assert(ntodelete < nbilinterms);
            todelete[ntodelete++] = bilinidx;
         }

         if( nxvars == 0 ) /* all (remaining) x_j seem to be unbounded */
            break;

         assert(!SCIPisInfinity(scip, -SCIPintervalGetInf(xbndszero)));
         assert(!SCIPisInfinity(scip,  SCIPintervalGetSup(xbndszero)));
         assert(!SCIPisInfinity(scip, -SCIPintervalGetInf(xbndsone)));
         assert(!SCIPisInfinity(scip,  SCIPintervalGetSup(xbndsone)));

#ifdef SCIP_DEBUG
         if( SCIPintervalGetInf(xbndszero) != SCIPintervalGetInf(xbndsone) || /*lint !e777*/
            +SCIPintervalGetSup(xbndszero) != SCIPintervalGetSup(xbndsone) ) /*lint !e777*/
         {
            SCIPdebugMessage("got different bounds for y = 0: [%g, %g] and y = 1: [%g, %g]\n", xbndszero.inf, xbndszero.sup, xbndsone.inf, xbndsone.sup);
         }
#endif

         if( nxvars == 1 && conshdlrdata->empathy4and >= 1 && SCIPvarIsBinary(xvars[0]) )
         {
            /* product of two binary variables, replace by auxvar and AND constraint */
            /* add auxiliary variable z */
            (void)SCIPsnprintf(name, SCIP_MAXSTRLEN, "prod%s_%s_%s", SCIPvarGetName(y), SCIPvarGetName(xvars[0]), SCIPconsGetName(cons));
            SCIP_CALL( SCIPcreateVar(scip, &auxvar, name, 0.0, 1.0, 0.0, SCIP_VARTYPE_IMPLINT,
                  auxvarinitial, auxvarremovable, NULL, NULL, NULL, NULL, NULL) );
            SCIP_CALL( SCIPaddVar(scip, auxvar) );

#ifdef SCIP_DEBUG_SOLUTION
            if( SCIPdebugIsMainscip(scip) )
            {
               SCIP_Real var0val;
               SCIP_Real var1val;
               SCIP_CALL( SCIPdebugGetSolVal(scip, xvars[0], &var0val) );
               SCIP_CALL( SCIPdebugGetSolVal(scip, y, &var1val) );
               SCIP_CALL( SCIPdebugAddSolVal(scip, auxvar, var0val * var1val) );
            }
#endif

            /* add constraint z = x and y */
            xvars[1] = y;
            (void)SCIPsnprintf(name, SCIP_MAXSTRLEN, "%sAND%s_%s", SCIPvarGetName(y), SCIPvarGetName(xvars[0]), SCIPconsGetName(cons));
            SCIP_CALL( SCIPcreateConsAnd(scip, &auxcons, name, auxvar, 2, xvars,
                  SCIPconsIsInitial(cons) && conshdlrdata->binreforminitial,
                  SCIPconsIsSeparated(cons), SCIPconsIsEnforced(cons), SCIPconsIsChecked(cons),
                  SCIPconsIsPropagated(cons),  SCIPconsIsLocal(cons), SCIPconsIsModifiable(cons),
                  SCIPconsIsDynamic(cons), SCIPconsIsRemovable(cons), SCIPconsIsStickingAtNode(cons)) );
            SCIP_CALL( SCIPaddCons(scip, auxcons) );
            SCIPdebugMessage("added AND constraint: ");
            SCIPdebugPrintCons(scip, auxcons, NULL);
            SCIP_CALL( SCIPreleaseCons(scip, &auxcons) );
            ++*naddconss;

            /* add linear term coef*auxvar */
            SCIP_CALL( addLinearCoef(scip, cons, auxvar, xcoef[0]) );

            /* forget about auxvar */
            SCIP_CALL( SCIPreleaseVar(scip, &auxvar) );
         }
         else
         {
            /* product of binary variable with more than one binary or with continuous variables or with binary and user did not like AND -> replace by auxvar and linear constraints */
            SCIP_Real scale;

            /* scale auxiliary constraint by some nice value,
             * if all coefficients are integral, take a value that preserves integrality (-> gcd), so we can make the auxiliary variable impl. integer
             */
            if( integral )
            {
               scale = (SCIP_Real)gcd;
               assert(scale >= 1.0);
            }
            else if( nxvars == 1 )
            {
               /* scaling by the only coefficient gives auxiliary variable = x * y, which thus will be implicit integral provided y is not continuous */
               assert(mincoef == maxcoef);  /*lint !e777 */
               scale = mincoef;
               integral = SCIPvarGetType(xvars[0]) < SCIP_VARTYPE_CONTINUOUS;
            }
            else
            {
               scale = 1.0;
               if( maxcoef < 0.5 )
                  scale = maxcoef;
               if( mincoef > 2.0 )
                  scale = mincoef;
               if( scale != 1.0 )
                  scale = SCIPselectSimpleValue(scale / 2.0, 1.5 * scale, MAXDNOM);
            }
            assert(scale > 0.0);
            assert(!SCIPisInfinity(scip, scale));

            /* if x-term is always negative for y = 1, negate scale so we get a positive auxiliary variable; maybe this is better sometimes? */
            if( !SCIPisPositive(scip, SCIPintervalGetSup(xbndsone)) )
               scale = -scale;

            SCIPdebugMessage("binary reformulation using scale %g, nxvars = %d, integral = %u\n", scale, nxvars, integral);
            if( scale != 1.0 )
            {
               SCIPintervalDivScalar(SCIPinfinity(scip), &xbndszero, xbndszero, scale);
               SCIPintervalDivScalar(SCIPinfinity(scip), &xbndsone,  xbndsone, scale);
               for( k = 0; k < nxvars; ++k )
                  xcoef[k] /= scale;
            }

            /* add auxiliary variable z */
            if( nxvars == 1 )
               (void)SCIPsnprintf(name, SCIP_MAXSTRLEN, "prod%s_%s_%s", SCIPvarGetName(y), SCIPvarGetName(xvars[0]), SCIPconsGetName(cons));
            else
               (void)SCIPsnprintf(name, SCIP_MAXSTRLEN, "prod%s_%s_more_%s", SCIPvarGetName(y), SCIPvarGetName(xvars[0]), SCIPconsGetName(cons));
            SCIP_CALL( SCIPcreateVar(scip, &auxvar, name, MIN(0., SCIPintervalGetInf(xbndsone)), MAX(0., SCIPintervalGetSup(xbndsone)),
                  0.0, integral ? SCIP_VARTYPE_IMPLINT : SCIP_VARTYPE_CONTINUOUS,
                  auxvarinitial, auxvarremovable, NULL, NULL, NULL, NULL, NULL) );
            SCIP_CALL( SCIPaddVar(scip, auxvar) );

            /* compute value of auxvar in debug solution */
#ifdef SCIP_DEBUG_SOLUTION
            if( SCIPdebugIsMainscip(scip) )
            {
               SCIP_Real debugval;
               SCIP_Real varval;

               SCIP_CALL( SCIPdebugGetSolVal(scip, y, &varval) );
               if( SCIPisZero(scip, varval) )
               {
                  SCIP_CALL( SCIPdebugAddSolVal(scip, auxvar, 0.0) );
               }
               else
               {
                  assert(SCIPisEQ(scip, varval, 1.0));

                  debugval = 0.0;
                  for( k = 0; k < nxvars; ++k )
                  {
                     SCIP_CALL( SCIPdebugGetSolVal(scip, xvars[k], &varval) );
                     debugval += xcoef[k] * varval;
                  }
                  SCIP_CALL( SCIPdebugAddSolVal(scip, auxvar, debugval) );
               }
            }
#endif

            /* add auxiliary constraints
             * it seems to be advantageous to make the varbound constraints initial and the linear constraints not initial
             * maybe because it is more likely that a binary variable takes value 0 instead of 1, and thus the varbound constraints
             * are more often active, compared to the linear constraints added below
             * also, the varbound constraints are more sparse than the linear cons
             */
            if( SCIPisNegative(scip, SCIPintervalGetInf(xbndsone)) )
            {
               /* add 0 <= z - xbndsone.inf * y constraint (as varbound constraint) */
               if( nxvars == 1 )
                  (void)SCIPsnprintf(name, SCIP_MAXSTRLEN, "linreform%s*%s_%s_1", SCIPvarGetName(y), SCIPvarGetName(xvars[0]), SCIPconsGetName(cons));
               else
                  (void)SCIPsnprintf(name, SCIP_MAXSTRLEN, "linreform%s*%s*more_%s_1", SCIPvarGetName(y), SCIPvarGetName(xvars[0]), SCIPconsGetName(cons));
               SCIP_CALL( SCIPcreateConsVarbound(scip, &auxcons, name, auxvar, y, -SCIPintervalGetInf(xbndsone), 0.0, SCIPinfinity(scip),
                     SCIPconsIsInitial(cons) /*&& conshdlrdata->binreforminitial*/,
                     SCIPconsIsSeparated(cons), SCIPconsIsEnforced(cons), SCIPconsIsChecked(cons),
                     SCIPconsIsPropagated(cons),  SCIPconsIsLocal(cons), SCIPconsIsModifiable(cons),
                     SCIPconsIsDynamic(cons), SCIPconsIsRemovable(cons), SCIPconsIsStickingAtNode(cons)) );
               SCIP_CALL( SCIPaddCons(scip, auxcons) );
               SCIPdebugMessage("added varbound constraint: ");
               SCIPdebugPrintCons(scip, auxcons, NULL);
               SCIP_CALL( SCIPreleaseCons(scip, &auxcons) );
               ++*naddconss;
            }
            if( SCIPisPositive(scip, SCIPintervalGetSup(xbndsone)) )
            {
               /* add z - xbndsone.sup * y <= 0 constraint (as varbound constraint) */
               if( nxvars == 1 )
                  (void)SCIPsnprintf(name, SCIP_MAXSTRLEN, "linreform%s*%s_%s_2", SCIPvarGetName(y), SCIPvarGetName(xvars[0]), SCIPconsGetName(cons));
               else
                  (void)SCIPsnprintf(name, SCIP_MAXSTRLEN, "linreform%s*%s*more_%s_2", SCIPvarGetName(y), SCIPvarGetName(xvars[0]), SCIPconsGetName(cons));
               SCIP_CALL( SCIPcreateConsVarbound(scip, &auxcons, name, auxvar, y, -SCIPintervalGetSup(xbndsone), -SCIPinfinity(scip), 0.0,
                     SCIPconsIsInitial(cons) /*&& conshdlrdata->binreforminitial*/,
                     SCIPconsIsSeparated(cons), SCIPconsIsEnforced(cons), SCIPconsIsChecked(cons),
                     SCIPconsIsPropagated(cons),  SCIPconsIsLocal(cons), SCIPconsIsModifiable(cons),
                     SCIPconsIsDynamic(cons), SCIPconsIsRemovable(cons), SCIPconsIsStickingAtNode(cons)) );
               SCIP_CALL( SCIPaddCons(scip, auxcons) );
               SCIPdebugMessage("added varbound constraint: ");
               SCIPdebugPrintCons(scip, auxcons, NULL);
               SCIP_CALL( SCIPreleaseCons(scip, &auxcons) );
               ++*naddconss;
            }

            /* add xbndszero.inf <= sum_i a_i*x_i + xbndszero.inf * y - z constraint */
            xvars[nxvars]   = y;
            xvars[nxvars+1] = auxvar;
            xcoef[nxvars]   = SCIPintervalGetInf(xbndszero);
            xcoef[nxvars+1] = -1;

            if( nxvars == 1 )
               (void)SCIPsnprintf(name, SCIP_MAXSTRLEN, "linreform%s*%s_%s_3", SCIPvarGetName(y), SCIPvarGetName(xvars[0]), SCIPconsGetName(cons));
            else
               (void)SCIPsnprintf(name, SCIP_MAXSTRLEN, "linreform%s*%s*more_%s_3", SCIPvarGetName(y), SCIPvarGetName(xvars[0]), SCIPconsGetName(cons));
            SCIP_CALL( SCIPcreateConsLinear(scip, &auxcons, name, nxvars+2, xvars, xcoef, SCIPintervalGetInf(xbndszero), SCIPinfinity(scip),
                  SCIPconsIsInitial(cons) && conshdlrdata->binreforminitial,
                  SCIPconsIsSeparated(cons), SCIPconsIsEnforced(cons), SCIPconsIsChecked(cons),
                  SCIPconsIsPropagated(cons),  SCIPconsIsLocal(cons), SCIPconsIsModifiable(cons),
                  SCIPconsIsDynamic(cons), SCIPconsIsRemovable(cons), SCIPconsIsStickingAtNode(cons)) );
            SCIP_CALL( SCIPaddCons(scip, auxcons) );
            SCIPdebugMessage("added linear constraint: ");
            SCIPdebugPrintCons(scip, auxcons, NULL);
            SCIP_CALL( SCIPreleaseCons(scip, &auxcons) );
            ++*naddconss;

            /* add sum_i a_i*x_i + xbndszero.sup * y - z <= xbndszero.sup constraint */
            xcoef[nxvars] = SCIPintervalGetSup(xbndszero);

            if( nxvars == 1 )
               (void)SCIPsnprintf(name, SCIP_MAXSTRLEN, "linreform%s*%s_%s_4", SCIPvarGetName(y), SCIPvarGetName(xvars[0]), SCIPconsGetName(cons));
            else
               (void)SCIPsnprintf(name, SCIP_MAXSTRLEN, "linreform%s*%s*more_%s_4", SCIPvarGetName(y), SCIPvarGetName(xvars[0]), SCIPconsGetName(cons));
            SCIP_CALL( SCIPcreateConsLinear(scip, &auxcons, name, nxvars+2, xvars, xcoef, -SCIPinfinity(scip), SCIPintervalGetSup(xbndszero),
                  SCIPconsIsInitial(cons) && conshdlrdata->binreforminitial,
                  SCIPconsIsSeparated(cons), SCIPconsIsEnforced(cons), SCIPconsIsChecked(cons),
                  SCIPconsIsPropagated(cons),  SCIPconsIsLocal(cons), SCIPconsIsModifiable(cons),
                  SCIPconsIsDynamic(cons), SCIPconsIsRemovable(cons), SCIPconsIsStickingAtNode(cons)) );
            SCIP_CALL( SCIPaddCons(scip, auxcons) );
            SCIPdebugMessage("added linear constraint: ");
            SCIPdebugPrintCons(scip, auxcons, NULL);
            SCIP_CALL( SCIPreleaseCons(scip, &auxcons) );
            ++*naddconss;

            /* add linear term scale*auxvar to this constraint */
            SCIP_CALL( addLinearCoef(scip, cons, auxvar, scale) );

            /* forget about auxvar */
            SCIP_CALL( SCIPreleaseVar(scip, &auxvar) );
         }
      }
      while( j < nbilinterms );

      /* remove bilinear terms that have been replaced */
      SCIP_CALL( removeBilinearTermsPos(scip, cons, ntodelete, todelete) );
   }
   SCIPdebugMessage("resulting quadratic constraint: ");
   SCIPdebugPrintCons(scip, cons, NULL);

   SCIPfreeBufferArrayNull(scip, &xvars);
   SCIPfreeBufferArrayNull(scip, &xcoef);
   SCIPfreeBufferArrayNull(scip, &todelete);

   return SCIP_OKAY;
}

/** tries to automatically convert a quadratic constraint (or a part of it) into a more specific and more specialized constraint */
static
SCIP_RETCODE presolveUpgrade(
   SCIP*                 scip,               /**< SCIP data structure */
   SCIP_CONSHDLR*        conshdlr,           /**< constraint handler data structure */
   SCIP_CONS*            cons,               /**< source constraint to try to convert */
   SCIP_Bool*            upgraded,           /**< buffer to store whether constraint was upgraded */
   int*                  nupgdconss,         /**< buffer to increase if constraint was upgraded */
   int*                  naddconss           /**< buffer to increase with number of additional constraints created during upgrade */
   )
{
   SCIP_CONSHDLRDATA* conshdlrdata;
   SCIP_CONSDATA* consdata;
   SCIP_VAR* var;
   SCIP_Real lincoef;
   SCIP_Real quadcoef;
   SCIP_Real lb;
   SCIP_Real ub;
   int nbinlin;
   int nbinquad;
   int nintlin;
   int nintquad;
   int nimpllin;
   int nimplquad;
   int ncontlin;
   int ncontquad;
   SCIP_Bool integral;
   int i;
   int j;
   SCIP_CONS** upgdconss;
   int upgdconsssize;
   int nupgdconss_;

   assert(scip != NULL);
   assert(conshdlr != NULL);
   assert(cons != NULL);
   assert(!SCIPconsIsModifiable(cons));
   assert(upgraded   != NULL);
   assert(nupgdconss != NULL);
   assert(naddconss  != NULL);

   *upgraded = FALSE;

   nupgdconss_ = 0;

   conshdlrdata = SCIPconshdlrGetData(conshdlr);
   assert(conshdlrdata != NULL);

   /* if there are no upgrade methods, we can also stop */
   if( conshdlrdata->nquadconsupgrades == 0 )
      return SCIP_OKAY;

   upgdconsssize = 2;
   SCIP_CALL( SCIPallocBufferArray(scip, &upgdconss, upgdconsssize) );

   consdata = SCIPconsGetData(cons);
   assert(consdata != NULL);

   /* calculate some statistics on quadratic constraint */
   nbinlin   = 0;
   nbinquad  = 0;
   nintlin   = 0;
   nintquad  = 0;
   nimpllin  = 0;
   nimplquad = 0;
   ncontlin  = 0;
   ncontquad = 0;
   integral  = TRUE;
   for( i = 0; i < consdata->nlinvars; ++i )
   {
      var = consdata->linvars[i];
      lincoef = consdata->lincoefs[i];
      lb  = SCIPvarGetLbLocal(var);
      ub  = SCIPvarGetUbLocal(var);
      assert(!SCIPisZero(scip, lincoef));

      switch( SCIPvarGetType(var) )
      {
      case SCIP_VARTYPE_BINARY:
         if( !SCIPisZero(scip, lb) || !SCIPisZero(scip, ub) )
            integral = integral && SCIPisIntegral(scip, lincoef);
         nbinlin++;
         break;
      case SCIP_VARTYPE_INTEGER:
         if( !SCIPisZero(scip, lb) || !SCIPisZero(scip, ub) )
            integral = integral && SCIPisIntegral(scip, lincoef);
         nintlin++;
         break;
      case SCIP_VARTYPE_IMPLINT:
         if( !SCIPisZero(scip, lb) || !SCIPisZero(scip, ub) )
            integral = integral && SCIPisIntegral(scip, lincoef);
         nimpllin++;
         break;
      case SCIP_VARTYPE_CONTINUOUS:
         integral = integral && SCIPisRelEQ(scip, lb, ub) && SCIPisIntegral(scip, lincoef * lb);
         ncontlin++;
         break;
      default:
         SCIPerrorMessage("unknown variable type\n");
         return SCIP_INVALIDDATA;
      }
   }

   for( i = 0; i < consdata->nquadvars; ++i )
   {
      var = consdata->quadvarterms[i].var;
      lincoef  = consdata->quadvarterms[i].lincoef;
      quadcoef = consdata->quadvarterms[i].sqrcoef;
      lb  = SCIPvarGetLbLocal(var);
      ub  = SCIPvarGetUbLocal(var);

      switch( SCIPvarGetType(var) )
      {
      case SCIP_VARTYPE_BINARY:
         if( !SCIPisZero(scip, lb) || !SCIPisZero(scip, ub) )
            integral = integral && SCIPisIntegral(scip, lincoef) && SCIPisIntegral(scip, quadcoef);
         nbinquad++;
         break;
      case SCIP_VARTYPE_INTEGER:
         if( !SCIPisZero(scip, lb) || !SCIPisZero(scip, ub) )
            integral = integral && SCIPisIntegral(scip, lincoef) && SCIPisIntegral(scip, quadcoef);
         nintquad++;
         break;
      case SCIP_VARTYPE_IMPLINT:
         if( !SCIPisZero(scip, lb) || !SCIPisZero(scip, ub) )
            integral = integral && SCIPisIntegral(scip, lincoef) && SCIPisIntegral(scip, quadcoef);
         nimplquad++;
         break;
      case SCIP_VARTYPE_CONTINUOUS:
         integral = integral && SCIPisRelEQ(scip, lb, ub) && SCIPisIntegral(scip, lincoef * lb + quadcoef * lb * lb);
         ncontquad++;
         break;
      default:
         SCIPerrorMessage("unknown variable type\n");
         return SCIP_INVALIDDATA;
      }
   }

   if( integral )
   {
      for( i = 0; i < consdata->nbilinterms && integral; ++i )
      {
         if( SCIPvarGetType(consdata->bilinterms[i].var1) < SCIP_VARTYPE_CONTINUOUS && SCIPvarGetType(consdata->bilinterms[i].var2) < SCIP_VARTYPE_CONTINUOUS )
            integral = integral && SCIPisIntegral(scip, consdata->bilinterms[i].coef);
         else
            integral = FALSE;
      }
   }

   /* call the upgrading methods */

   SCIPdebugMessage("upgrading quadratic constraint <%s> (%d upgrade methods):\n",
      SCIPconsGetName(cons), conshdlrdata->nquadconsupgrades);
   SCIPdebugMessage(" binlin=%d binquad=%d intlin=%d intquad=%d impllin=%d implquad=%d contlin=%d contquad=%d integral=%u\n",
      nbinlin, nbinquad, nintlin, nintquad, nimpllin, nimplquad, ncontlin, ncontquad, integral);
   SCIPdebugPrintCons(scip, cons, NULL);

   /* try all upgrading methods in priority order in case the upgrading step is enable  */
   for( i = 0; i < conshdlrdata->nquadconsupgrades; ++i )
   {
      if( !conshdlrdata->quadconsupgrades[i]->active )
         continue;

      SCIP_CALL( conshdlrdata->quadconsupgrades[i]->quadconsupgd(scip, cons,
            nbinlin, nbinquad, nintlin, nintquad, nimpllin, nimplquad, ncontlin, ncontquad, integral,
            &nupgdconss_, upgdconss, upgdconsssize) );

      while( nupgdconss_ < 0 )
      {
         /* upgrade function requires more memory: resize upgdconss and call again */
         assert(-nupgdconss_ > upgdconsssize);
         upgdconsssize = -nupgdconss_;
         SCIP_CALL( SCIPreallocBufferArray(scip, &upgdconss, -nupgdconss_) );

         SCIP_CALL( conshdlrdata->quadconsupgrades[i]->quadconsupgd(scip, cons,
               nbinlin, nbinquad, nintlin, nintquad, nimpllin, nimplquad, ncontlin, ncontquad, integral,
               &nupgdconss_, upgdconss, upgdconsssize) );

         assert(nupgdconss_ != 0);
      }

      if( nupgdconss_ > 0 )
      {
         /* got upgrade */
         SCIPdebugPrintCons(scip, cons, NULL);
         SCIPdebugMessage(" -> upgraded to %d constraints:\n", nupgdconss_);

         /* add the upgraded constraints to the problem and forget them */
         for( j = 0; j < nupgdconss_; ++j )
         {
            SCIPdebugPrintf("\t");
            SCIPdebugPrintCons(scip, upgdconss[j], NULL);

            SCIP_CALL( SCIPaddCons(scip, upgdconss[j]) );      /*lint !e613*/
            SCIP_CALL( SCIPreleaseCons(scip, &upgdconss[j]) ); /*lint !e613*/
         }

         /* count the first upgrade constraint as constraint upgrade and the remaining ones as added constraints */
         *nupgdconss += 1;
         *naddconss += nupgdconss_ - 1;
         *upgraded = TRUE;

         /* delete upgraded constraint */
         SCIPdebugMessage("delete constraint <%s> after upgrade\n", SCIPconsGetName(cons));
         SCIP_CALL( dropVarEvents(scip, conshdlrdata->eventhdlr, cons) );
         SCIP_CALL( SCIPdelCons(scip, cons) );

         break;
      }
   }

   SCIPfreeBufferArray(scip, &upgdconss);

   return SCIP_OKAY;
}

/** helper function for presolveDisaggregate */
static
SCIP_RETCODE presolveDisaggregateMarkComponent(
   SCIP*                 scip,               /**< SCIP data structure */
   SCIP_CONSDATA*        consdata,           /**< constraint data */
   int                   quadvaridx,         /**< index of quadratic variable to mark */
   SCIP_HASHMAP*         var2component,      /**< variables to components mapping */
   int                   componentnr         /**< the component number to mark to */ 
   )
{
   SCIP_QUADVARTERM* quadvarterm;
   SCIP_VAR* othervar;
   int othervaridx;
   int i;

   assert(consdata != NULL);
   assert(quadvaridx >= 0);
   assert(quadvaridx < consdata->nquadvars);
   assert(var2component != NULL);
   assert(componentnr >= 0);

   quadvarterm = &consdata->quadvarterms[quadvaridx];

   if( SCIPhashmapExists(var2component, quadvarterm->var) )
   {
      /* if we saw the variable before, then it should have the same component number */
      assert((int)(size_t)SCIPhashmapGetImage(var2component, quadvarterm->var) == componentnr);
      return SCIP_OKAY;
   }

   /* assign component number to variable */
   SCIP_CALL( SCIPhashmapInsert(var2component, quadvarterm->var, (void*)(size_t)componentnr) );

   /* assign same component number to all variables this variable is multiplied with */
   for( i = 0; i < quadvarterm->nadjbilin; ++i )
   {
      othervar = consdata->bilinterms[quadvarterm->adjbilin[i]].var1 == quadvarterm->var ?
         consdata->bilinterms[quadvarterm->adjbilin[i]].var2 : consdata->bilinterms[quadvarterm->adjbilin[i]].var1;
      SCIP_CALL( consdataFindQuadVarTerm(scip, consdata, othervar, &othervaridx) );
      assert(othervaridx >= 0);
      SCIP_CALL( presolveDisaggregateMarkComponent(scip, consdata, othervaridx, var2component, componentnr) );
   }

   return SCIP_OKAY;
}

/** for quadratic constraints that consists of a sum of quadratic terms, disaggregates the sum into a set of constraints by introducing auxiliary variables */
static
SCIP_RETCODE presolveDisaggregate(
   SCIP*                 scip,               /**< SCIP data structure */
   SCIP_CONSHDLR*        conshdlr,           /**< constraint handler data structure */
   SCIP_CONS*            cons,               /**< source constraint to try to convert */
   int*                  naddconss           /**< pointer to counter of added constraints */
   )
{
   SCIP_CONSDATA* consdata;
   SCIP_HASHMAP* var2component;
   int ncomponents;
   int i;
   int comp;
   SCIP_CONS** auxconss;
   SCIP_VAR** auxvars;
   SCIP_Real* auxcoefs;
   char name[SCIP_MAXSTRLEN];

   assert(scip != NULL);
   assert(conshdlr != NULL);
   assert(cons != NULL);
   assert(naddconss != NULL);

   consdata = SCIPconsGetData(cons);
   assert(consdata != NULL);

   /* make sure there are no quadratic variables without coefficients */
   SCIP_CALL( mergeAndCleanBilinearTerms(scip, cons) );
   SCIP_CALL( mergeAndCleanQuadVarTerms(scip, cons) );

   if( consdata->nquadvars <= 1 )
      return SCIP_OKAY;

   /* sort quadratic variable terms here, so we can later search in it without reordering the array */
   SCIP_CALL( consdataSortQuadVarTerms(scip, consdata) );

   /* check how many quadratic terms with non-overlapping variables we have
    * in other words, the number of components in the sparsity graph of the quadratic term matrix */
   ncomponents = 0;
   SCIP_CALL( SCIPhashmapCreate(&var2component, SCIPblkmem(scip), SCIPcalcHashtableSize(consdata->nquadvars)) );
   for( i = 0; i < consdata->nquadvars; ++i )
   {
      /* if variable was marked already, skip it */
      if( SCIPhashmapExists(var2component, (void*)consdata->quadvarterms[i].var) )
         continue;

      SCIP_CALL( presolveDisaggregateMarkComponent(scip, consdata, i, var2component, ncomponents) );
      ++ncomponents;
   }
   assert(ncomponents >= 1);

   /* if there is only one component, we cannot disaggregate
    * @todo we could still split the constraint into several while keeping the number of variables sharing several constraints as small as possible
    */
   if( ncomponents == 1 )
   {
      SCIPhashmapFree(&var2component);
      return SCIP_OKAY;
   }

   SCIP_CALL( SCIPallocBufferArray(scip, &auxconss, ncomponents) );
   SCIP_CALL( SCIPallocBufferArray(scip, &auxvars,  ncomponents) );
   SCIP_CALL( SCIPallocBufferArray(scip, &auxcoefs, ncomponents) );

   /* create auxiliary variables and empty constraints for each component */
   for( comp = 0; comp < ncomponents; ++comp )
   {
      (void) SCIPsnprintf(name, SCIP_MAXSTRLEN, "%s_comp%d", SCIPconsGetName(cons), comp);

      SCIP_CALL( SCIPcreateVar(scip, &auxvars[comp], name, -SCIPinfinity(scip), SCIPinfinity(scip), 0.0,
            SCIP_VARTYPE_CONTINUOUS, SCIPconsIsInitial(cons), FALSE, NULL, NULL, NULL, NULL, NULL) );

      SCIP_CALL( SCIPcreateConsQuadratic2(scip, &auxconss[comp], name, 0, NULL, NULL, 0, NULL, 0, NULL,
            (SCIPisInfinity(scip, -consdata->lhs) ? -SCIPinfinity(scip) : 0.0),
            (SCIPisInfinity(scip,  consdata->rhs) ?  SCIPinfinity(scip) : 0.0),
            SCIPconsIsInitial(cons), SCIPconsIsSeparated(cons), SCIPconsIsEnforced(cons),
            SCIPconsIsChecked(cons), SCIPconsIsPropagated(cons), SCIPconsIsLocal(cons), SCIPconsIsModifiable(cons),
            SCIPconsIsDynamic(cons), SCIPconsIsRemovable(cons)) );

      auxcoefs[comp] = SCIPinfinity(scip);
   }

   /* add quadratic variables to each component constraint
    * delete adjacency information */
   for( i = 0; i < consdata->nquadvars; ++i )
   {
      comp = (int)(size_t) SCIPhashmapGetImage(var2component, consdata->quadvarterms[i].var);
      assert(comp >= 0);
      assert(comp < ncomponents);

      /* add variable term to corresponding constraint */
      SCIP_CALL( SCIPaddQuadVarQuadratic(scip, auxconss[comp], consdata->quadvarterms[i].var, consdata->quadvarterms[i].lincoef, consdata->quadvarterms[i].sqrcoef) );

      /* reduce coefficient of aux variable */
      if( !SCIPisZero(scip, consdata->quadvarterms[i].lincoef) && ABS(consdata->quadvarterms[i].lincoef) < auxcoefs[comp] )
         auxcoefs[comp] = REALABS(consdata->quadvarterms[i].lincoef);
      if( !SCIPisZero(scip, consdata->quadvarterms[i].sqrcoef) && ABS(consdata->quadvarterms[i].sqrcoef) < auxcoefs[comp] )
         auxcoefs[comp] = REALABS(consdata->quadvarterms[i].sqrcoef);

      SCIPfreeBlockMemoryArray(scip, &consdata->quadvarterms[i].adjbilin, consdata->quadvarterms[i].adjbilinsize);
      consdata->quadvarterms[i].nadjbilin = 0;
      consdata->quadvarterms[i].adjbilinsize = 0;
   }

   /* add bilinear terms to each component constraint */
   for( i = 0; i < consdata->nbilinterms; ++i )
   {
      comp = (int)(size_t) SCIPhashmapGetImage(var2component, consdata->bilinterms[i].var1);
      assert(comp == (int)(size_t) SCIPhashmapGetImage(var2component, consdata->bilinterms[i].var2));
      assert(!SCIPisZero(scip, consdata->bilinterms[i].coef));

      SCIP_CALL( SCIPaddBilinTermQuadratic(scip, auxconss[comp], 
            consdata->bilinterms[i].var1, consdata->bilinterms[i].var2, consdata->bilinterms[i].coef) );

      if( ABS(consdata->bilinterms[i].coef) < auxcoefs[comp] )
         auxcoefs[comp] = ABS(consdata->bilinterms[i].coef);
   }

   /* forget about bilinear terms in cons */
   SCIPfreeBlockMemoryArray(scip, &consdata->bilinterms, consdata->bilintermssize);
   consdata->nbilinterms = 0;
   consdata->bilintermssize = 0;

   /* remove quadratic variable terms from cons */
   for( i = consdata->nquadvars - 1; i >= 0; --i )
   {
      SCIP_CALL( delQuadVarTermPos(scip, cons, i) );
   }
   assert(consdata->nquadvars == 0);

   /* add auxiliary variables to auxiliary constraints
    * add aux vars and constraints to SCIP 
    * add aux vars to this constraint
    * @todo compute debug solution values and set for auxvars
    */
   SCIPdebugMessage("add %d constraints for disaggregation of quadratic constraint <%s>\n", ncomponents, SCIPconsGetName(cons));
   SCIP_CALL( consdataEnsureLinearVarsSize(scip, consdata, consdata->nlinvars + ncomponents) );
   for( comp = 0; comp < ncomponents; ++comp )
   {
      SCIP_CALL( SCIPaddLinearVarQuadratic(scip, auxconss[comp], auxvars[comp], -auxcoefs[comp]) );

      SCIP_CALL( SCIPaddVar(scip, auxvars[comp]) );

      SCIP_CALL( SCIPaddCons(scip, auxconss[comp]) );
      SCIPdebugPrintCons(scip, auxconss[comp], NULL);

      SCIP_CALL( addLinearCoef(scip, cons, auxvars[comp], auxcoefs[comp]) );

      SCIP_CALL( SCIPreleaseCons(scip, &auxconss[comp]) );
      SCIP_CALL( SCIPreleaseVar(scip, &auxvars[comp]) );
   }
   *naddconss += ncomponents;

   SCIPdebugPrintCons(scip, cons, NULL);

   SCIPfreeBufferArray(scip, &auxconss);
   SCIPfreeBufferArray(scip, &auxvars);
   SCIPfreeBufferArray(scip, &auxcoefs);
   SCIPhashmapFree(&var2component);

   return SCIP_OKAY;
}

#ifdef CHECKIMPLINBILINEAR
/** checks if there are bilinear terms x*y with a binary variable x and an implication x = {0,1} -> y = 0
 * in this case, the bilinear term can be removed (x=0 case) or replaced by y (x=1 case)
 */
static
SCIP_RETCODE presolveApplyImplications(
   SCIP*                 scip,               /**< SCIP data structure */
   SCIP_CONS*            cons,               /**< quadratic constraint */
   int*                  nbilinremoved       /**< buffer to store number of removed bilinear terms */
   )
{
   SCIP_CONSDATA* consdata;
   SCIP_VAR* x;
   SCIP_VAR* y;
   SCIP_INTERVAL implbnds;
   int i;
   int j;
   int k;

   assert(scip != NULL);
   assert(cons != NULL);
   assert(nbilinremoved != NULL);

   *nbilinremoved = 0;

   consdata = SCIPconsGetData(cons);
   assert(consdata != NULL);

   SCIPdebugMessage("apply implications in <%s>\n", SCIPconsGetName(cons));

   /* sort quadvarterms in case we need to search */
   SCIP_CALL( consdataSortQuadVarTerms(scip, consdata) );

   for( i = 0; i < consdata->nquadvars; ++i )
   {
      x = consdata->quadvarterms[i].var;
      assert(x != NULL);

      if( consdata->quadvarterms[i].nadjbilin == 0 )
         continue;

      if( !SCIPvarIsBinary(x) )
         continue;

      if( !SCIPvarIsActive(x) )
         continue;

      if( SCIPvarGetNImpls(x, TRUE) == 0 && SCIPvarGetNImpls(x, FALSE) == 0 )
         continue;

      for( j = 0; j < consdata->quadvarterms[i].nadjbilin; ++j )
      {
         k = consdata->quadvarterms[i].adjbilin[j];
         assert(k >= 0);
         assert(k < consdata->nbilinterms);

         if( consdata->bilinterms[k].coef == 0.0 )
            continue;

         y = consdata->bilinterms[k].var1 == x ? consdata->bilinterms[k].var2 : consdata->bilinterms[k].var1;
         assert(x != y);

         getImpliedBounds(x, TRUE, y, &implbnds);
         if( SCIPisZero(scip, implbnds.inf) && SCIPisZero(scip, implbnds.sup) )
         {
            /* if x = 1 implies y = 0, then we can remove the bilinear term x*y, since it is always 0
             * we only set the coefficient to 0.0 here and mark the bilinterms as not merged */
            SCIPdebugMessage("remove bilinear term %g<%s><%s> from <%s> due to implication\n", consdata->bilinterms[k].coef, SCIPvarGetName(x), SCIPvarGetName(y), SCIPconsGetName(cons));
            consdata->bilinterms[k].coef = 0.0;
            consdata->bilinmerged = FALSE;
            ++*nbilinremoved;
            continue;
         }

         getImpliedBounds(x, FALSE, y, &implbnds);
         if( SCIPisZero(scip, implbnds.inf) && SCIPisZero(scip, implbnds.sup) )
         {
            /* if x = 0 implies y = 0, then we can replace the bilinear term x*y by y
             * we only move the coefficient to the linear coef of y here and mark the bilinterms as not merged */
            SCIPdebugMessage("replace bilinear term %g<%s><%s> by %g<%s> in <%s> due to implication\n", consdata->bilinterms[k].coef, SCIPvarGetName(x), SCIPvarGetName(y), consdata->bilinterms[k].coef, SCIPvarGetName(y), SCIPconsGetName(cons));
            assert(consdata->quadvarssorted);
            SCIP_CALL( SCIPaddQuadVarLinearCoefQuadratic(scip, cons, y, consdata->bilinterms[k].coef) );
            consdata->bilinterms[k].coef = 0.0;
            consdata->bilinmerged = FALSE;
            ++*nbilinremoved;
         }
      }
   }

   if( *nbilinremoved > 0 )
   {
      SCIP_CALL( mergeAndCleanBilinearTerms(scip, cons) );

      /* invalidate nonlinear row */
      if( consdata->nlrow != NULL )
      {
         SCIP_CALL( SCIPreleaseNlRow(scip, &consdata->nlrow) );
      }

      consdata->ispropagated  = FALSE;
      consdata->ispresolved   = FALSE;
      consdata->iscurvchecked = FALSE;
   }

   consdata->isimpladded = FALSE;

   return SCIP_OKAY;
}
#endif

/** checks a quadratic constraint for convexity and/or concavity without checking multivariate functions */
static
void checkCurvatureEasy(
   SCIP*                 scip,               /**< SCIP data structure */
   SCIP_CONS*            cons,               /**< quadratic constraint */
   SCIP_Bool*            determined,         /**< pointer to store whether the curvature could be determined */
   SCIP_Bool             checkmultivariate   /**< whether curvature will be checked later on for multivariate functions */
   )
{
   SCIP_CONSDATA* consdata;
   int nquadvars;

   assert(scip != NULL);
   assert(cons != NULL);
   assert(determined != NULL);

   consdata = SCIPconsGetData(cons);
   assert(consdata != NULL);

   nquadvars = consdata->nquadvars;
   *determined = TRUE;

   if( consdata->iscurvchecked )
      return;

   SCIPdebugMessage("Checking curvature of constraint <%s> without multivariate functions\n", SCIPconsGetName(cons));

   if( nquadvars == 1 )
   {
      assert(consdata->nbilinterms == 0);
      consdata->isconvex      = !SCIPisNegative(scip, consdata->quadvarterms[0].sqrcoef);
      consdata->isconcave     = !SCIPisPositive(scip, consdata->quadvarterms[0].sqrcoef);
      consdata->iscurvchecked = TRUE;
   }
   else if( nquadvars == 0 )
   {
      consdata->isconvex = TRUE;
      consdata->isconcave = TRUE;
      consdata->iscurvchecked = TRUE;
   }
   else if( consdata->nbilinterms == 0 )
   {
      int v;

      consdata->isconvex = TRUE;
      consdata->isconcave = TRUE;

      for( v = nquadvars - 1; v >= 0; --v )
      {
         consdata->isconvex  = consdata->isconvex  && !SCIPisNegative(scip, consdata->quadvarterms[v].sqrcoef);
         consdata->isconcave = consdata->isconcave && !SCIPisPositive(scip, consdata->quadvarterms[v].sqrcoef);
      }

      consdata->iscurvchecked = TRUE;
   }
   else if( !checkmultivariate )
   {
      consdata->isconvex  = FALSE;
      consdata->isconcave = FALSE;
      consdata->iscurvchecked = TRUE;
   }
   else
      *determined = FALSE;
}

/** checks a quadratic constraint for convexity and/or concavity */
static
SCIP_RETCODE checkCurvature(
   SCIP*                 scip,               /**< SCIP data structure */
   SCIP_CONS*            cons,               /**< quadratic constraint */
   SCIP_Bool             checkmultivariate   /**< whether curvature should also be checked for multivariate functions */
   )
{
   SCIP_CONSDATA* consdata;
   double*        matrix;
   SCIP_HASHMAP*  var2index;
   int            i;
   int            n;
   int            nn;
   int            row;
   int            col;
   double*        alleigval;
   SCIP_Bool      determined;

   assert(scip != NULL);
   assert(cons != NULL);

   consdata = SCIPconsGetData(cons);
   assert(consdata != NULL);

   n = consdata->nquadvars;

   if( consdata->iscurvchecked )
      return SCIP_OKAY;

   /* easy checks for curvature detection */
   checkCurvatureEasy(scip, cons, &determined, checkmultivariate);

   /* if curvature was already detected stop */
   if( determined )
      return SCIP_OKAY;

   SCIPdebugMessage("Checking curvature of constraint <%s> with multivariate functions\n", SCIPconsGetName(cons));

   if( n == 2 )
   {
      /* compute eigenvalues by hand */
      assert(consdata->nbilinterms == 1);
      consdata->isconvex =
         consdata->quadvarterms[0].sqrcoef >= 0 &&
         consdata->quadvarterms[1].sqrcoef >= 0 &&
         4 * consdata->quadvarterms[0].sqrcoef * consdata->quadvarterms[1].sqrcoef >= consdata->bilinterms[0].coef * consdata->bilinterms[0].coef;
      consdata->isconcave = 
         consdata->quadvarterms[0].sqrcoef <= 0 &&
         consdata->quadvarterms[1].sqrcoef <= 0 &&
         4 * consdata->quadvarterms[0].sqrcoef * consdata->quadvarterms[1].sqrcoef >= consdata->bilinterms[0].coef * consdata->bilinterms[0].coef;
      consdata->iscurvchecked = TRUE;
      return SCIP_OKAY;
   }

   /* lower triangular of quadratic term matrix */
   nn = n * n;
   SCIP_CALL( SCIPallocBufferArray(scip, &matrix, nn) );
   BMSclearMemoryArray(matrix, nn);

   consdata->isconvex  = TRUE;
   consdata->isconcave = TRUE;

   SCIP_CALL( SCIPhashmapCreate(&var2index, SCIPblkmem(scip), SCIPcalcHashtableSize(5 * n)) );
   for( i = 0; i < n; ++i )
   {
      if( consdata->quadvarterms[i].nadjbilin > 0 )
      {
         SCIP_CALL( SCIPhashmapInsert(var2index, consdata->quadvarterms[i].var, (void*)(size_t)i) );
         matrix[i*n + i] = consdata->quadvarterms[i].sqrcoef;
      }
      /* nonzero elements on diagonal tell a lot about convexity/concavity */
      if( SCIPisNegative(scip, consdata->quadvarterms[i].sqrcoef) )
         consdata->isconvex  = FALSE;
      if( SCIPisPositive(scip, consdata->quadvarterms[i].sqrcoef) )
         consdata->isconcave = FALSE;
   }

   if( !consdata->isconvex && !consdata->isconcave )
   {
      SCIPfreeBufferArray(scip, &matrix);
      SCIPhashmapFree(&var2index);
      consdata->iscurvchecked = TRUE;
      return SCIP_OKAY;
   }

   if( SCIPisIpoptAvailableIpopt() )
   {
      for( i = 0; i < consdata->nbilinterms; ++i )
      {
         assert(SCIPhashmapExists(var2index, consdata->bilinterms[i].var1));
         assert(SCIPhashmapExists(var2index, consdata->bilinterms[i].var2));
         row = (int)(size_t)SCIPhashmapGetImage(var2index, consdata->bilinterms[i].var1);
         col = (int)(size_t)SCIPhashmapGetImage(var2index, consdata->bilinterms[i].var2);
         if( row < col )
            matrix[row * n + col] = consdata->bilinterms[i].coef/2;
         else
            matrix[col * n + row] = consdata->bilinterms[i].coef/2;
      }

      SCIP_CALL( SCIPallocBufferArray(scip, &alleigval, n) );
      /* @todo Can we compute only min and max eigen value?
       * @todo Can we estimate the numerical error? 
       * @todo Trying a cholesky factorization may be much faster. 
       */
      if( LapackDsyev(FALSE, n, matrix, alleigval) != SCIP_OKAY )
      {
         SCIPwarningMessage(scip, "Failed to compute eigenvalues of quadratic coefficient matrix of constraint %s. Assuming matrix is indefinite.\n", SCIPconsGetName(cons));
         consdata->isconvex = FALSE;
         consdata->isconcave = FALSE;
      }
      else
      {
         /* deconvexification reformulates a stricly convex quadratic function in binaries such that it becomes not-strictly convex
          * by adding the -lambda*(x^2-x) terms for lambda the smallest eigenvalue of the matrix
          * the result is still a convex form "but less so" (ref. papers by Guignard et.al.), but with hopefully tighter value for the continuous relaxation
          */
#ifdef DECONVEXIFY
         SCIP_Bool allbinary;
         printf("cons <%s>[%g,%g] spectrum = [%g,%g]\n", SCIPconsGetName(cons), consdata->lhs, consdata->rhs, alleigval[0], alleigval[n-1]);
#endif
         consdata->isconvex  &= !SCIPisNegative(scip, alleigval[0]);   /*lint !e514*/
         consdata->isconcave &= !SCIPisPositive(scip, alleigval[n-1]); /*lint !e514*/
         consdata->iscurvchecked = TRUE;
#ifdef DECONVEXIFY
         for( i = 0; i < consdata->nquadvars; ++i )
            if( !SCIPvarIsBinary(consdata->quadvarterms[i].var) )
               break;
         allbinary = i == consdata->nquadvars;

         if( !SCIPisInfinity(scip, consdata->rhs) && alleigval[0] > 0.1 && allbinary )
         {
            printf("deconvexify cons <%s> by shifting hessian by %g\n", SCIPconsGetName(cons), alleigval[0]);
            for( i = 0; i < consdata->nquadvars; ++i )
            {
               consdata->quadvarterms[i].sqrcoef -= alleigval[0];
               consdata->quadvarterms[i].lincoef += alleigval[0];
            }
         }

         if( !SCIPisInfinity(scip, consdata->lhs) && alleigval[n-1] < -0.1 && allbinary )
         {
            printf("deconcavify cons <%s> by shifting hessian by %g\n", SCIPconsGetName(cons), alleigval[n-1]);
            for( i = 0; i < consdata->nquadvars; ++i )
            {
               consdata->quadvarterms[i].sqrcoef -= alleigval[n-1];
               consdata->quadvarterms[i].lincoef += alleigval[n-1];
            }
         }
#endif
      }

      SCIPfreeBufferArray(scip, &alleigval);
   }
   else
   {
      consdata->isconvex = FALSE;
      consdata->isconcave = FALSE;
      consdata->iscurvchecked = TRUE; /* set to TRUE since it does not help to repeat this procedure again and again (that will not bring Ipopt in) */
   }

   SCIPhashmapFree(&var2index);
   SCIPfreeBufferArray(scip, &matrix);

   return SCIP_OKAY;
}

/** check whether indefinite constraint function is factorable and store corresponding coefficients */
static
SCIP_RETCODE checkFactorable(
   SCIP*                 scip,               /**< SCIP data structure */
   SCIP_CONS*            cons                /**< constraint */
   )
{
   SCIP_BILINTERM* bilinterm;
   SCIP_CONSDATA* consdata;
   SCIP_Real* a;
   SCIP_Real* eigvals;
   SCIP_Real sigma1;
   SCIP_Real sigma2;
   SCIP_Bool success;
   int n;
   int i;
   int idx1;
   int idx2;
   int posidx;
   int negidx;

   assert(scip != NULL);
   assert(cons != NULL);

   consdata = SCIPconsGetData(cons);
   assert(consdata != NULL);
   assert(consdata->factorleft == NULL);
   assert(consdata->factorright == NULL);

   /* we don't need this if there are no bilinear terms */
   if( consdata->nbilinterms == 0 )
      return SCIP_OKAY;

   /* write constraint as lhs <= linear + x'^T A x' <= rhs where x' = (x,1) and
    * A = ( Q     b/2 )
    *     ( b^T/2  0  )
    * compute an eigenvalue factorization of A and check if there are one positive and one negative eigenvalue
    * if so, then let sigma1^2 and -sigma2^2 be these eigenvalues and v1 and v2 be the first two rows of the inverse eigenvector matrix
    * thus, x'^T A x' = sigma1^2 (v1^T x')^2 - sigma2^2 (v2^T x')^2
    *                 = (sigma1 (v1^T x') - sigma2 (v2^T x')) * (sigma1 (v1^T x') + sigma2 (v2^T x'))
    * we then store sigma1 v1^T - sigma2 v2^T as left factor coef, and sigma1 v1^T + sigma2 v2^T as right factor coef
    */

   /* if we already know that there are only positive or only negative eigenvalues, then don't try */
   if( consdata->iscurvchecked && (consdata->isconvex || consdata->isconcave) )
      return SCIP_OKAY;

   n = consdata->nquadvars + 1;

   /* @todo handle case n=3 explicitly */

   /* skip too large matrices */
   if( n > 50 )
      return SCIP_OKAY;

   /* need routine to compute eigenvalues/eigenvectors */
   if( !SCIPisIpoptAvailableIpopt() )
      return SCIP_OKAY;

   SCIP_CALL( consdataSortQuadVarTerms(scip, consdata) );

   SCIP_CALL( SCIPallocBufferArray(scip, &a, n*n) );
   BMSclearMemoryArray(a, n*n);

   /* set lower triangular entries of A corresponding to bilinear terms */
   for( i = 0; i < consdata->nbilinterms; ++i )
   {
      bilinterm = &consdata->bilinterms[i];

      SCIP_CALL( consdataFindQuadVarTerm(scip, consdata, bilinterm->var1, &idx1) );
      SCIP_CALL( consdataFindQuadVarTerm(scip, consdata, bilinterm->var2, &idx2) );
      assert(idx1 >= 0);
      assert(idx2 >= 0);
      assert(idx1 != idx2);

      a[MIN(idx1,idx2) * n + MAX(idx1,idx2)] = bilinterm->coef / 2.0;
   }

   /* set lower triangular entries of A corresponding to square and linear terms */
   for( i = 0; i < consdata->nquadvars; ++i )
   {
      a[i*n + i]   = consdata->quadvarterms[i].sqrcoef;
      a[i*n + n-1] = consdata->quadvarterms[i].lincoef / 2.0;
   }

   SCIP_CALL( SCIPallocBufferArray(scip, &eigvals, n) );
   if( LapackDsyev(TRUE, n, a, eigvals) != SCIP_OKAY )
   {
      SCIPdebugMessage("Failed to compute eigenvalues and eigenvectors of augmented quadratic form matrix for constraint <%s>.\n", SCIPconsGetName(cons));
      goto CLEANUP;
   }

   /* check if there is exactly one positive and one negative eigenvalue */
   posidx = -1;
   negidx = -1;
   for( i = 0; i < n; ++i )
   {
      if( SCIPisPositive(scip, eigvals[i]) )
      {
         if( posidx == -1 )
            posidx = i;
         else
            break;
      }
      else if( SCIPisNegative(scip, eigvals[i]) )
      {
         if( negidx == -1 )
            negidx = i;
         else
            break;
      }
   }
   if( i < n || posidx == -1 || negidx == -1 )
   {
      SCIPdebugMessage("Augmented quadratic form of constraint <%s> is not factorable.\n", SCIPconsGetName(cons));
      goto CLEANUP;
   }
   assert(SCIPisPositive(scip, eigvals[posidx]));
   assert(SCIPisNegative(scip, eigvals[negidx]));

   /* compute factorleft and factorright */
   SCIP_CALL( SCIPallocBlockMemoryArray(scip, &consdata->factorleft,  consdata->nquadvars + 1) );
   SCIP_CALL( SCIPallocBlockMemoryArray(scip, &consdata->factorright, consdata->nquadvars + 1) );

   /* eigenvectors are stored in a, inverse eigenvector matrix is transposed of a
    * it seems that v1 and v2 are at &a[posidx*n] and &a[negidx*n]
    */
   sigma1 = sqrt( eigvals[posidx]);
   sigma2 = sqrt(-eigvals[negidx]);
   for( i = 0; i < n; ++i )
   {
      consdata->factorleft[i]  = sigma1 * a[posidx * n + i] - sigma2 * a[negidx * n + i];
      consdata->factorright[i] = sigma1 * a[posidx * n + i] + sigma2 * a[negidx * n + i];
      /* set almost-zero elements to zero */
      if( SCIPisZero(scip, consdata->factorleft[i]) )
         consdata->factorleft[i] = 0.0;
      if( SCIPisZero(scip, consdata->factorright[i]) )
         consdata->factorright[i] = 0.0;
   }

#ifdef SCIP_DEBUG
   SCIPdebugMessage("constraint <%s> has factorable quadratic form: (%g", SCIPconsGetName(cons), consdata->factorleft[n-1]);
   for( i = 0; i < consdata->nquadvars; ++i )
   {
      if( consdata->factorleft[i] != 0.0 )
         SCIPdebugPrintf(" %+g<%s>", consdata->factorleft[i], SCIPvarGetName(consdata->quadvarterms[i].var));
   }
   SCIPdebugPrintf(") * (%g", consdata->factorright[n-1]);
   for( i = 0; i < consdata->nquadvars; ++i )
   {
      if( consdata->factorright[i] != 0.0 )
         SCIPdebugPrintf(" %+g<%s>", consdata->factorright[i], SCIPvarGetName(consdata->quadvarterms[i].var));
   }
   SCIPdebugPrintf(")\n");
#endif

   /* check whether factorleft * factorright^T is matrix of augmented quadratic form
    * we check here only the nonzero entries from the quadratic form
    */
   success = TRUE;

   /* check bilinear terms */
   for( i = 0; i < consdata->nbilinterms; ++i )
   {
      bilinterm = &consdata->bilinterms[i];

      SCIP_CALL( consdataFindQuadVarTerm(scip, consdata, bilinterm->var1, &idx1) );
      SCIP_CALL( consdataFindQuadVarTerm(scip, consdata, bilinterm->var2, &idx2) );

      if( !SCIPisRelEQ(scip, consdata->factorleft[idx1] * consdata->factorright[idx2] + consdata->factorleft[idx2] * consdata->factorright[idx1], bilinterm->coef) )
      {
         success = FALSE;
         break;
      }
   }

   /* set lower triangular entries of A corresponding to square and linear terms */
   for( i = 0; i < consdata->nquadvars; ++i )
   {
      if( !SCIPisRelEQ(scip, consdata->factorleft[i] * consdata->factorright[i], consdata->quadvarterms[i].sqrcoef) )
      {
         success = FALSE;
         break;
      }

      if( !SCIPisRelEQ(scip, consdata->factorleft[n-1] * consdata->factorright[i] + consdata->factorleft[i] * consdata->factorright[n-1], consdata->quadvarterms[i].lincoef) )
      {
         success = FALSE;
         break;
      }
   }

   if( !success )
   {
      SCIPdebugMessage("Factorization not accurate enough. Dropping it.\n");
      SCIPfreeBlockMemoryArray(scip, &consdata->factorleft,  consdata->nquadvars + 1);
      SCIPfreeBlockMemoryArray(scip, &consdata->factorright, consdata->nquadvars + 1);
   }

 CLEANUP:
   SCIPfreeBufferArray(scip, &a);
   SCIPfreeBufferArray(scip, &eigvals);

   return SCIP_OKAY;
}

/** gets maximal absolute value in gradient of quadratic function */
static
SCIP_Real getGradientMaxElement(
   SCIP*                 scip,               /**< SCIP data structure */
   SCIP_CONS*            cons,               /**< constraint */
   SCIP_SOL*             sol                 /**< solution or NULL if LP solution should be used */
   )
{
   SCIP_CONSDATA* consdata;
   SCIP_Real      maxelem;
   SCIP_Real      g;
   int            i, j, k;
   SCIP_VAR*      var;

   assert(scip != NULL);
   assert(cons != NULL);

   consdata = SCIPconsGetData(cons);
   assert(consdata != NULL);

   if( SCIPgetStage(scip) != SCIP_STAGE_SOLVING )
   {
      maxelem = 0.0;
      for( i = 0; i < consdata->nlinvars; ++i )
         if( REALABS(consdata->lincoefs[i]) > maxelem )
            maxelem = REALABS(consdata->lincoefs[i]);
   }
   else
   {
      maxelem = consdata->lincoefsmax;
   }

   for( i = 0; i < consdata->nquadvars; ++i )
   {
      var = consdata->quadvarterms[i].var;
      assert(!SCIPisInfinity(scip,  SCIPgetSolVal(scip, sol, var)));
      assert(!SCIPisInfinity(scip, -SCIPgetSolVal(scip, sol, var)));
      g  =       consdata->quadvarterms[i].lincoef;
      g += 2.0 * consdata->quadvarterms[i].sqrcoef * SCIPgetSolVal(scip, sol, var);
      for( j = 0; j < consdata->quadvarterms[i].nadjbilin; ++j )
      {
         k = consdata->quadvarterms[i].adjbilin[j];
         if( consdata->bilinterms[k].var1 == var )
            g += consdata->bilinterms[k].coef * SCIPgetSolVal(scip, sol, consdata->bilinterms[k].var2);
         else
            g += consdata->bilinterms[k].coef * SCIPgetSolVal(scip, sol, consdata->bilinterms[k].var1);
      }
      if( REALABS(g) > maxelem )
         maxelem = REALABS(g);
   }

   return maxelem;
}

/** computes activity and violation of a constraint */
static
SCIP_RETCODE computeViolation(
   SCIP*                 scip,               /**< SCIP data structure */
   SCIP_CONSHDLR*        conshdlr,           /**< constraint handler */
   SCIP_CONS*            cons,               /**< constraint */
   SCIP_SOL*             sol                 /**< solution or NULL if LP solution should be used */
   )
{  /*lint --e{666}*/
   SCIP_CONSHDLRDATA* conshdlrdata;
   SCIP_CONSDATA* consdata;
   SCIP_Real varval;
   SCIP_Real varval2;
   SCIP_VAR* var;
   SCIP_VAR* var2;
   int i;
   int j;

   assert(scip != NULL);
   assert(cons != NULL);

   conshdlrdata = SCIPconshdlrGetData(conshdlr);
   assert(conshdlrdata != NULL);

   consdata = SCIPconsGetData(cons);
   assert(consdata != NULL);

   consdata->activity = 0.0;
   varval = 0.0;

   /* @todo Take better care of variables at +/- infinity: e.g., run instance waste in debug mode with a short timelimit (30s). */
   for( i = 0; i < consdata->nlinvars; ++i )
   {
      var = consdata->linvars[i];
      varval = SCIPgetSolVal(scip, sol, var);

      if( SCIPisInfinity(scip, REALABS(varval)) )
      {
         consdata->activity = SCIPinfinity(scip);
         if( !SCIPisInfinity(scip, -consdata->lhs) )
            consdata->lhsviol = SCIPinfinity(scip);
         if( !SCIPisInfinity(scip,  consdata->rhs) )
            consdata->rhsviol = SCIPinfinity(scip);
         return SCIP_OKAY;
      }

      /* project onto local box, in case the LP solution is slightly outside the bounds (which is not our job to enforce) */
      if( sol == NULL )
      {
         /* with non-initial columns, this might fail because variables can shortly be a column variable before entering the LP and have value 0.0 in this case
         assert(SCIPisFeasGE(scip, varval, SCIPvarGetLbLocal(var)));
         assert(SCIPisFeasLE(scip, varval, SCIPvarGetUbLocal(var)));
         */
         varval = MAX(SCIPvarGetLbLocal(var), MIN(SCIPvarGetUbLocal(var), varval));
      }

      consdata->activity += consdata->lincoefs[i] * varval;
   }

   for( j = 0; j < consdata->nquadvars; ++j )
   {
      var = consdata->quadvarterms[j].var;
      varval = SCIPgetSolVal(scip, sol, var);
      if( SCIPisInfinity(scip, REALABS(varval)) )
      {
         consdata->activity = SCIPinfinity(scip);
         if( !SCIPisInfinity(scip, -consdata->lhs) )
            consdata->lhsviol = SCIPinfinity(scip);
         if( !SCIPisInfinity(scip,  consdata->rhs) )
            consdata->rhsviol = SCIPinfinity(scip);
         return SCIP_OKAY;
      }

      /* project onto local box, in case the LP solution is slightly outside the bounds (which is not our job to enforce) */
      if( sol == NULL )
      {
         /* with non-initial columns, this might fail because variables can shortly be a column variable before entering the LP and have value 0.0 in this case
         assert(SCIPisFeasGE(scip, varval, SCIPvarGetLbLocal(var)));
         assert(SCIPisFeasLE(scip, varval, SCIPvarGetUbLocal(var)));
         */
         varval = MAX(SCIPvarGetLbLocal(var), MIN(SCIPvarGetUbLocal(var), varval));
      }

      consdata->activity += (consdata->quadvarterms[j].lincoef + consdata->quadvarterms[j].sqrcoef * varval) * varval;
   }

   for( j = 0; j < consdata->nbilinterms; ++j )
   {
      var = consdata->bilinterms[j].var1;
      var2 = consdata->bilinterms[j].var2;
      varval = SCIPgetSolVal(scip, sol, var);
      varval2 = SCIPgetSolVal(scip, sol, var2);

      /* project onto local box, in case the LP solution is slightly outside the bounds (which is not our job to enforce) */
      if( sol == NULL )
      {
#if 0 /* with non-initial columns, this might fail because variables can shortly be a column variable before entering the LP and have value 0.0 in this case */
         assert(SCIPisFeasGE(scip, varval, SCIPvarGetLbLocal(var)));
         assert(SCIPisFeasLE(scip, varval, SCIPvarGetUbLocal(var)));
#endif
         varval = MAX(SCIPvarGetLbLocal(var), MIN(SCIPvarGetUbLocal(var), varval));

#if 0 /* with non-initial columns, this might fail because variables can shortly be a column variable before entering the LP and have value 0.0 in this case */
         assert(SCIPisFeasGE(scip, varval2, SCIPvarGetLbLocal(var2)));
         assert(SCIPisFeasLE(scip, varval2, SCIPvarGetUbLocal(var2)));
#endif
         varval2 = MAX(SCIPvarGetLbLocal(var2), MIN(SCIPvarGetUbLocal(var2), varval2));
      }

      consdata->activity += consdata->bilinterms[j].coef * varval * varval2;
   }

   /* compute absolute violation left hand side */
   if( consdata->activity < consdata->lhs && !SCIPisInfinity(scip, -consdata->lhs) )
      consdata->lhsviol = consdata->lhs - consdata->activity;
   else
      consdata->lhsviol = 0.0;

   /* compute absolute violation right hand side */
   if( consdata->activity > consdata->rhs && !SCIPisInfinity(scip,  consdata->rhs) )
      consdata->rhsviol = consdata->activity - consdata->rhs;
   else
      consdata->rhsviol = 0.0;

   switch( conshdlrdata->scaling )
   {
   case 'o' :
      /* no scaling */
      break;

   case 'g' :
      /* scale by sup-norm of gradient in current point */
      if( consdata->lhsviol > 0.0 || consdata->rhsviol > 0.0 )
      {
         SCIP_Real norm;
         norm = getGradientMaxElement(scip, cons, sol);
         if( norm > 1.0 )
         {
            consdata->lhsviol /= norm;
            consdata->rhsviol /= norm;
         }
      }
      break;

   case 's' :
      /* scale by left/right hand side of constraint */
      if( consdata->lhsviol > 0.0 )
         consdata->lhsviol /= MAX(1.0, REALABS(consdata->lhs));

      if( consdata->rhsviol > 0.0 )
         consdata->rhsviol /= MAX(1.0, REALABS(consdata->rhs));

      break;

   default :
      SCIPerrorMessage("Unknown scaling method '%c'.", conshdlrdata->scaling);
      SCIPABORT();
      return SCIP_INVALIDDATA;  /*lint !e527*/
   }

   return SCIP_OKAY;
}

/** computes violation of a set of constraints */
static
SCIP_RETCODE computeViolations(
   SCIP*                 scip,               /**< SCIP data structure */
   SCIP_CONSHDLR*        conshdlr,           /**< constraint handler */
   SCIP_CONS**           conss,              /**< constraints */
   int                   nconss,             /**< number of constraints */
   SCIP_SOL*             sol,                /**< solution or NULL if LP solution should be used */
   SCIP_CONS**           maxviolcon          /**< buffer to store constraint with largest violation, or NULL if solution is feasible */
   )
{
   SCIP_CONSDATA* consdata;
   SCIP_Real      viol;
   SCIP_Real      maxviol;
   int            c;

   assert(scip != NULL);
   assert(conss != NULL || nconss == 0);
   assert(maxviolcon != NULL);

   *maxviolcon = NULL;

   maxviol = 0.0;

   for( c = 0; c < nconss; ++c )
   {
      assert(conss != NULL);
      assert(conss[c] != NULL);

      SCIP_CALL( computeViolation(scip, conshdlr, conss[c], sol) );

      consdata = SCIPconsGetData(conss[c]);
      assert(consdata != NULL);

      viol = MAX(consdata->lhsviol, consdata->rhsviol);
      if( viol > maxviol && SCIPisGT(scip, viol, SCIPfeastol(scip)) )
      {
         maxviol = viol;
         *maxviolcon = conss[c];
      }
   }

   return SCIP_OKAY;
}

/** tries to compute cut for multleft * <coefleft, x'> * multright <= rhs / (multright * <coefright, x'>) where x'=(x,1) */
static
void generateCutFactorableDo(
   SCIP*                 scip,               /**< SCIP data structure */
   SCIP_CONS*            cons,               /**< constraint */
   SCIP_Real*            ref,                /**< reference solution where to generate the cut */
   SCIP_Real             multleft,           /**< multiplicator on lhs */
   SCIP_Real*            coefleft,           /**< coefficient for factor on lhs */
   SCIP_Real             multright,          /**< multiplicator on both sides */
   SCIP_Real*            coefright,          /**< coefficient for factor that goes to rhs */
   SCIP_Real             rightminactivity,   /**< minimal activity of <coefright, x> */
   SCIP_Real             rightmaxactivity,   /**< maximal activity of <coefright, x> */
   SCIP_Real             rhs,                /**< denominator on rhs */
   SCIP_Real*            cutcoef,            /**< array to store cut coefficients for quadratic variables */
   SCIP_Real*            cutrhs,             /**< buffer to store cut rhs */
   SCIP_Bool*            islocal,            /**< buffer to set to TRUE if local information was used */
   SCIP_Bool*            success,            /**< buffer to indicate whether a cut was successfully computed */
   char*                 name                /**< buffer to store name of cut */
   )
{
   SCIP_CONSDATA* consdata;
   SCIP_Real constant;
   int i;

   assert(cutcoef != NULL);
   assert(rightminactivity * multright > 0.0);
   assert(rightmaxactivity * multright > 0.0);
   assert(multright == 1.0 || multright == -1.0);

   consdata = SCIPconsGetData(cons);
   assert(consdata != NULL);

   if( rhs > 0.0 )
   {
      /* if rhs > 0.0, then rhs / (multright * <coefright, x'>) is convex, thus need secant:
       *  1 / multright*<coefright, x'> <= 1/minact + 1/maxact - 1/(minact * maxact) multright*<coefright, x'>
       *  where [minact, maxact] = multright * [rightminactivity, rightmaxactivity]
       *
       * assuming multright is either -1 or 1, and substituting gives
       *  multright/rightminactivity + multright/rightmaxactivity  - multright/(rightminactivity * rightmaxactivity) *<coefright, x'>
       *
       * multiplying by rhs, gives the estimate
       *  rhs / (multright * <coefright, x'>) <= rhs * multright * (1/rightminactivity + 1/rightmaxactivity - 1/(rightminactivity * rightmaxactivity) * <coefright, x'>)
       */

      /* cannot do if unbounded */
      if( SCIPisInfinity(scip, rightmaxactivity) )
      {
         *success = FALSE;
         return;
      }

      assert(SCIPisFeasLE(scip, rightminactivity, rightmaxactivity));

      constant = multleft * multright * coefleft[consdata->nquadvars];
      constant -= rhs * multright * (1.0 / rightminactivity + 1.0 / rightmaxactivity);
      constant += rhs * multright * coefright[consdata->nquadvars] / (rightminactivity * rightmaxactivity);

      for( i = 0; i < consdata->nquadvars; ++i )
      {
         cutcoef[i] = multleft * multright * coefleft[i];
         cutcoef[i] += rhs * multright / (rightminactivity * rightmaxactivity) * coefright[i];
      }

      (void) SCIPsnprintf(name, SCIP_MAXSTRLEN, "%s_factorablesecant_%d", SCIPconsGetName(cons), SCIPgetNLPs(scip));
   }
   else
   {
      SCIP_Real refvalue;

      /* if rhs < 0.0, then rhs / (multright * <coefright, x'>) is convex, thus need linearization:
       *     rhs / (multright * <coefright, x'>)
       *  <= rhs / (multright * <coefright, ref'>) - rhs / (multright * <coefright, ref'>)^2 * (multright * <coefright, x'> - multright * <coefright, ref'>)
       *   = 2*rhs / (multright * <coefright, ref'>) - rhs / (multright * <coefright, ref'>)^2 * (multright * <coefright, x'>)
       *
       *  where ref' = (ref, 1)
       */

      /* compute <coefright, ref'> */
      refvalue = coefright[consdata->nquadvars];
      for( i = 0; i < consdata->nquadvars; ++i )
         refvalue += coefright[i] * ref[i];

      /* should not happen, since we checked activity of <coefright,x> before, and assume ref within bounds */
      assert(!SCIPisZero(scip, refvalue));

      constant  = multleft * multright * coefleft[consdata->nquadvars];
      constant -= 2.0 * rhs / (multright * refvalue);
      constant += rhs / (refvalue * refvalue) * multright * coefright[consdata->nquadvars];

      for( i = 0; i < consdata->nquadvars; ++i )
      {
         cutcoef[i] = multleft * multright * coefleft[i];
         cutcoef[i] += rhs / (refvalue * refvalue) * multright * coefright[i];
      }

      (void) SCIPsnprintf(name, SCIP_MAXSTRLEN, "%s_factorablelinearization_%d", SCIPconsGetName(cons), SCIPgetNLPs(scip));
   }

   *cutrhs = -constant;

   /* @todo does not always need to be local */
   *islocal = TRUE;
   *success = TRUE;
}

/** tries to generate a cut if constraint quadratic function is factorable and there are no linear variables
 * (ax+b)(cx+d) <= rhs and cx+d >= 0 -> (ax+b) <= rhs / (cx+d), where the right hand side is concave and can be linearized
 */
static
SCIP_RETCODE generateCutFactorable(
   SCIP*                 scip,               /**< SCIP data structure */
   SCIP_CONS*            cons,               /**< constraint */
   SCIP_SIDETYPE         violside,           /**< for which side a cut should be generated */
   SCIP_Real*            ref,                /**< reference solution where to generate the cut */
   SCIP_Real*            cutcoef,            /**< array to store cut coefficients for quadratic variables */
   SCIP_Real*            cutlhs,             /**< buffer to store cut lhs */
   SCIP_Real*            cutrhs,             /**< buffer to store cut rhs */
   SCIP_Bool*            islocal,            /**< buffer to set to TRUE if local information was used */
   SCIP_Bool*            success,            /**< buffer to indicate whether a cut was successfully computed */
   char*                 name                /**< buffer to store name of cut */
   )
{
   SCIP_CONSDATA* consdata;
   SCIP_Real leftminactivity;
   SCIP_Real leftmaxactivity;
   SCIP_Real rightminactivity;
   SCIP_Real rightmaxactivity;
   SCIP_Real multleft;
   SCIP_Real multright;
   SCIP_Real rhs;
   int i;

   assert(scip != NULL);
   assert(cons != NULL);
   assert(ref  != NULL);
   assert(cutcoef != NULL);
   assert(cutlhs  != NULL);
   assert(cutrhs  != NULL);
   assert(islocal != NULL);
   assert(success != NULL);
   assert(name != NULL);

   consdata = SCIPconsGetData(cons);
   assert(consdata != NULL);
   assert(consdata->nlinvars == 0);
   assert(consdata->factorleft != NULL);
   assert(consdata->factorright != NULL);

   *success = FALSE;
   *cutlhs = -SCIPinfinity(scip);

   leftminactivity = consdata->factorleft[consdata->nquadvars];
   leftmaxactivity = consdata->factorleft[consdata->nquadvars];
   rightminactivity = consdata->factorright[consdata->nquadvars];
   rightmaxactivity = consdata->factorright[consdata->nquadvars];
   for( i = 0; i < consdata->nquadvars; ++i )
   {
      if( !SCIPisInfinity(scip, -leftminactivity) )
      {
         if( consdata->factorleft[i] > 0.0 )
         {
            if( SCIPisInfinity(scip, -SCIPvarGetLbLocal(consdata->quadvarterms[i].var)) )
               leftminactivity = -SCIPinfinity(scip);
            else
               leftminactivity += consdata->factorleft[i] * SCIPvarGetLbLocal(consdata->quadvarterms[i].var);
         }
         else if( consdata->factorleft[i] < 0.0 )
         {
            if( SCIPisInfinity(scip, SCIPvarGetUbLocal(consdata->quadvarterms[i].var)) )
               leftminactivity = -SCIPinfinity(scip);
            else
               leftminactivity += consdata->factorleft[i] * SCIPvarGetUbLocal(consdata->quadvarterms[i].var);
         }
      }
      if( !SCIPisInfinity(scip, leftmaxactivity) )
      {
         if( consdata->factorleft[i] > 0.0 )
         {
            if( SCIPisInfinity(scip, SCIPvarGetUbLocal(consdata->quadvarterms[i].var)) )
               leftmaxactivity = SCIPinfinity(scip);
            else
               leftmaxactivity += consdata->factorleft[i] * SCIPvarGetUbLocal(consdata->quadvarterms[i].var);
         }
         else if( consdata->factorleft[i] < 0.0 )
         {
            if( SCIPisInfinity(scip, -SCIPvarGetLbLocal(consdata->quadvarterms[i].var)) )
               leftmaxactivity = SCIPinfinity(scip);
            else
               leftmaxactivity += consdata->factorleft[i] * SCIPvarGetLbLocal(consdata->quadvarterms[i].var);
         }
      }

      if( !SCIPisInfinity(scip, -rightminactivity) )
      {
         if( consdata->factorright[i] > 0.0 )
         {
            if( SCIPisInfinity(scip, -SCIPvarGetLbLocal(consdata->quadvarterms[i].var)) )
               rightminactivity = -SCIPinfinity(scip);
            else
               rightminactivity += consdata->factorright[i] * SCIPvarGetLbLocal(consdata->quadvarterms[i].var);
         }
         else if( consdata->factorright[i] < 0.0 )
         {
            if( SCIPisInfinity(scip, SCIPvarGetUbLocal(consdata->quadvarterms[i].var)) )
               rightminactivity = -SCIPinfinity(scip);
            else
               rightminactivity += consdata->factorright[i] * SCIPvarGetUbLocal(consdata->quadvarterms[i].var);
         }
      }
      if( !SCIPisInfinity(scip, rightmaxactivity) )
      {
         if( consdata->factorright[i] > 0.0 )
         {
            if( SCIPisInfinity(scip, SCIPvarGetUbLocal(consdata->quadvarterms[i].var)) )
               rightmaxactivity = SCIPinfinity(scip);
            else
               rightmaxactivity += consdata->factorright[i] * SCIPvarGetUbLocal(consdata->quadvarterms[i].var);
         }
         else if( consdata->factorright[i] < 0.0 )
         {
            if( SCIPisInfinity(scip, -SCIPvarGetLbLocal(consdata->quadvarterms[i].var)) )
               rightmaxactivity = SCIPinfinity(scip);
            else
               rightmaxactivity += consdata->factorright[i] * SCIPvarGetLbLocal(consdata->quadvarterms[i].var);
         }
      }
   }

   /* write violated constraints as multleft * factorleft * factorright <= rhs */
   if( violside == SCIP_SIDETYPE_RIGHT )
   {
      rhs = consdata->rhs;
      multleft = 1.0;
   }
   else
   {
      rhs = -consdata->lhs;
      multleft = -1.0;
   }

   if( SCIPisZero(scip, rhs) )
   {
      /* @todo do something for rhs == 0.0? */
      return SCIP_OKAY;
   }

   if( !SCIPisFeasPositive(scip, leftminactivity) && !SCIPisFeasNegative(scip, leftmaxactivity) )
   {
      /* left factor has 0 within activity bounds, or is very close, at least */
      if( !SCIPisFeasPositive(scip, rightminactivity) && !SCIPisFeasNegative(scip, rightmaxactivity) )
      {
         /* right factor also has 0 within activity bounds, or is very close, at least
          * -> cannot separate
          */
         return SCIP_OKAY;
      }

      /* write violated constraint as multleft * factorleft * multright * (multright * factorright) <= rhs
       *   such that multright * factorright > 0.0
       */
      if( rightminactivity < 0.0 )
         multright = -1.0;
      else
         multright =  1.0;

      /* generate cut for multleft * factorleft * multright <= rhs / (factorright * multright) */
      generateCutFactorableDo(scip, cons, ref, multleft, consdata->factorleft, multright, consdata->factorright, rightminactivity, rightmaxactivity, rhs, cutcoef, cutrhs, islocal, success, name);
   }
   else if( !SCIPisFeasPositive(scip, rightminactivity) && !SCIPisFeasNegative(scip, rightmaxactivity) )
   {
      /* left factor is bounded away from 0
       * right factor has 0 within activity bounds, or is very close, at least
       * -> so divide by left factor
       */

      /* write violated constraint as multleft * factorright * multright * (multright * factorleft) <= rhs
       *   such that multright * factorleft > 0.0
       */
      if( leftminactivity < 0.0 )
         multright = -1.0;
      else
         multright =  1.0;

      /* generate cut for multleft * factorright * multright <= rhs / (factorleft * multright) */
      generateCutFactorableDo(scip, cons, ref, multleft, consdata->factorright, multright, consdata->factorleft, leftminactivity, leftmaxactivity, rhs, cutcoef, cutrhs, islocal, success, name);
   }
   else if( SCIPisInfinity(scip, -leftminactivity) || SCIPisInfinity(scip, leftmaxactivity) ||
      (!SCIPisInfinity(scip, -rightminactivity) && !SCIPisInfinity(scip, rightmaxactivity) && rightmaxactivity - rightminactivity < leftmaxactivity - leftminactivity) )
   {
      /* both factors are bounded away from 0, but the right one has a smaller activity range, so divide by that one */

      /* write violated constraint as multleft * factorleft * multright * (multright * factorright) <= rhs
       *   such that multright * factorright > 0.0
       */
      if( rightminactivity < 0.0 )
         multright = -1.0;
      else
         multright =  1.0;

      /* generate cut for multleft * factorleft * multright <= rhs / (factorright * multright) */
      generateCutFactorableDo(scip, cons, ref, multleft, consdata->factorleft, multright, consdata->factorright, rightminactivity, rightmaxactivity, rhs, cutcoef, cutrhs, islocal, success, name);
   }
   else
   {
      /* both factors are bounded away from 0, but the left one has a smaller activity range, so divide by that one */

      /* write violated constraint as multleft * factorright * multright * (multright * factorleft) <= rhs
       *   such that multright * factorleft > 0.0
       */
      if( leftminactivity < 0.0 )
         multright = -1.0;
      else
         multright =  1.0;

      /* generate cut for multleft * factorright * multright <= rhs / (factorleft * multright) */
      generateCutFactorableDo(scip, cons, ref, multleft, consdata->factorright, multright, consdata->factorleft, leftminactivity, leftmaxactivity, rhs, cutcoef, cutrhs, islocal, success, name);
   }

   return SCIP_OKAY;
}

/* finds intersections of a parametric line (x,y) = (x0,y0) + t [(x1,y1) - (x0,y0)] on curves x*y = wl and x*y = wu
 * returns TRUE if unsuccessful and FALSE otherwise
 */
static
SCIP_Bool generateCutLTIfindIntersection(
   SCIP*                 scip,
   SCIP_Real             x0,
   SCIP_Real             y0_,
   SCIP_Real             x1,
   SCIP_Real             y1_,
   SCIP_Real             wl,
   SCIP_Real             wu,
   SCIP_Real*            xl,
   SCIP_Real*            yl,
   SCIP_Real*            xu,
   SCIP_Real*            yu
   )
{
   SCIP_Real a;
   SCIP_Real b;
   SCIP_Real c;
   SCIP_Real tl;
   SCIP_Real tu;

   assert(wl == SCIP_INVALID || (xl != NULL && yl != NULL));  /*lint !e777 */
   assert(wu == SCIP_INVALID || (xu != NULL && yu != NULL));  /*lint !e777 */

   /* The parametric line is of the form
    *
    *  x = x0 + t (x1-x0)
    *  y = y0 + t (y1-y0)
    *
    * and for that to satisfy xy = wl and xy = wu we must have
    *
    * x0 y0 + t [x0 (y1-y0) + y0 (x1-x0)] + t^2 (x1-x0) (y1-y0) = wl
    *                                                           = wu
    *
    * or a t^2 + b t + c - wl = 0 for proper values of a,b,c.
    *    a t^2 + b t + c - wu = 0
    *
    * Because of the way this procedure will be used, one of the two
    * solutions found we must always use the minimum nonnegative one
    */

   a = (x1 - x0) * (y1_ - y0_);
   c = x0 * y0_;
   b = x0 * y1_ + y0_ * x1 - 2.0 * c;

   tl = 0.0;
   tu = 0.0;

   if( !SCIPisZero(scip, (SCIP_Real)a) )
   {
      if( wl != SCIP_INVALID )  /*lint !e777 */
      {
         SCIP_Real tl1;
         SCIP_Real tl2;
         SCIP_Real denom;

         assert(b * b - 4.0 * a * (c - wl) >= 0.0);
         denom = sqrt(b * b - 4.0 * a * (c - wl));
         tl1 = (-b - denom) / (2.0 * a);
         tl2 = (-b + denom) / (2.0 * a);
         tl = (tl1 < 0.0) ? tl2 : tl1;
      }

      if( wu != SCIP_INVALID )  /*lint !e777 */
      {
         SCIP_Real tu1;
         SCIP_Real tu2;
         SCIP_Real denom;

         assert(b * b - 4.0 * a * (c - wu) >= 0.0);
         denom = sqrt(b * b - 4.0 * a * (c - wu));
         tu1 = (-b - denom) / (2.0 * a);
         tu2 = (-b + denom) / (2.0 * a);
         tu = (tu1 < 0.0) ? tu2 : tu1;
      }
   }
   else if( !SCIPisZero(scip, (SCIP_Real)b) )
   {
      if( wl != SCIP_INVALID )  /*lint !e777 */
         tl = (wl - c) / b;
      if( wu != SCIP_INVALID )  /*lint !e777 */
         tu = (wu - c) / b;
   }
   else
   {
      /* no or infinitely many solutions */
      return TRUE;
   }

   if( wl != SCIP_INVALID )  /*lint !e777 */
   {
      *xl = (SCIP_Real)(x0  + tl * (x1  - x0 ));
      *yl = (SCIP_Real)(y0_ + tl * (y1_ - y0_));

      if( !SCIPisRelEQ(scip, *xl * *yl, wl) )
      {
         SCIPdebugMessage("probable numerical difficulties, give up\n");
         return TRUE;
      }
   }

   if( wu != SCIP_INVALID )  /*lint !e777 */
   {
      *xu = (SCIP_Real)(x0  + tu * (x1 -  x0));
      *yu = (SCIP_Real)(y0_ + tu * (y1_ - y0_));

      if( !SCIPisRelEQ(scip, *xu * *yu, wu) )
      {
         SCIPdebugMessage("probable numerical difficulties, give up\n");
         return TRUE;
      }
   }

   return FALSE;
}

/* generate coefficients for a plane through points (x1, y1_, x1*y1) and (x2, y2, x2*y2)
 * such that intersecting it with one of them (the first if whichuse is FALSE, the second otherwise)
 * gives a tangent to the curve x*y = k
 *
 * returns TRUE on error and FALSE on success
 */
static
SCIP_Bool generateCutLTIgenMulCoeff(
   SCIP*                 scip,
   SCIP_Real             x1,
   SCIP_Real             y1_,
   SCIP_Real             x2,
   SCIP_Real             y2,
   SCIP_Bool             whichuse,
   SCIP_Real*            cx,
   SCIP_Real*            cy,
   SCIP_Real*            cw
   )
{
   SCIP_Real xd;
   SCIP_Real yd;
   SCIP_Real xo;
   SCIP_Real yo;

   assert(cx != NULL);
   assert(cy != NULL);
   assert(cw != NULL);

   /* the x-y slope of this constraint must be tangent to a curve x*y = k at (xD,yD) */
   if( !whichuse )
   {
      xd = x1;
      xo = x2;
      yd = y1_;
      yo = y2;
   }
   else
   {
      xd = x2;
      xo = x1;
      yd = y2;
      yo = y1_;
   }

   *cx = yd;
   *cy = xd;

   /* lift it so that it touches the other curve */

   /* if the two points are on the same curve, then no cut */
   if( SCIPisZero(scip, xo * yo - xd * yd) )
      return TRUE;

   /* should ALWAYS be negative */
   *cw = (2.0 * xd * yd - (*cx * xo + *cy * yo)) / (xo * yo - xd * yd);

   return FALSE;
}

/** computes coefficients of a lifted-tangent inequality for x*y = w
 * The code is an adaptation of the methods in exprMul-upperHull.cpp in Couenne/stable/0.4 rev773,
 * written by P. Belotti and licensed under Eclipse Public License.
 */
static
void generateCutLTIcomputeCoefs(
   SCIP*                 scip,               /**< SCIP data structure */
   SCIP_Real             xl,                 /**< lower bound on x */
   SCIP_Real             xu,                 /**< upper bound on x */
   SCIP_Real             x0,                 /**< reference point for x */
   SCIP_Real             yl,                 /**< lower bound on y */
   SCIP_Real             yu,                 /**< upper bound on y */
   SCIP_Real             y0_,                /**< reference point for y */
   SCIP_Real             wl,                 /**< lower bound on w */
   SCIP_Real             wu,                 /**< upper bound on w */
   SCIP_Real             w0,                 /**< reference point for w */
   SCIP_Real*            cx,                 /**< buffer where to store cut coefficient for x */
   SCIP_Real*            cy,                 /**< buffer where to store cut coefficient for y */
   SCIP_Real*            cw,                 /**< buffer where to store cut coefficient for w */
   SCIP_Real*            c0,                 /**< buffer where to store cut left-hand-side */
   SCIP_Bool*            success             /**< buffer where to indicate whether cut coefficients were computed */
   )
{
   SCIP_Bool flipx;
   SCIP_Bool flipy;
   SCIP_Bool flipw;
   SCIP_Real tmp;
   SCIP_Real xlow;
   SCIP_Real ylow;
   SCIP_Real xupp;
   SCIP_Real yupp;
   SCIP_Real c0x;
   SCIP_Real c0y;
   SCIP_Real c0w;

   assert(scip != NULL);
   assert(cx != NULL);
   assert(cy != NULL);
   assert(cw != NULL);
   assert(c0 != NULL);
   assert(success != NULL);

   *success = FALSE;
   *cx = 0.0;
   *cy = 0.0;
   *cw = 0.0;
   *c0 = 0.0;

   SCIPdebugMessage("entering points:\n");
   SCIPdebugMessage("x: %9g\t[%9g\t%9g]\n", x0, xl, xu);
   SCIPdebugMessage("y: %9g\t[%9g\t%9g]\n", y0_, yl, yu);
   SCIPdebugMessage("w: %9g\t[%9g\t%9g]\n", w0, wl, wu);

   /* generateCutLTI should have recognized these */
   assert(wl >= 0.0 || wu <= 0.0);
   assert(!SCIPisInfinity(scip, -wl));
   assert(!SCIPisInfinity(scip,  wu));

   assert(SCIPisFeasGE(scip, x0, xl));
   assert(SCIPisFeasLE(scip, x0, xu));
   assert(SCIPisFeasGE(scip, y0_, yl));
   assert(SCIPisFeasLE(scip, y0_, yu));

   /* preliminary bound tightening */
   if( wl >= 0.0 )
   {
      if( xl >= 0.0 || yl >= 0.0 || SCIPisLT(scip, xl * yl, wl) )
      {
         xl = MAX(xl, 0.0);
         yl = MAX(yl, 0.0);
      }
      else if( xu <= 0.0 || yu <= 0.0 || SCIPisLT(scip, xu * yu, wl) )
      {
         xu = MIN(xu, 0.0);
         yu = MIN(yu, 0.0);
      }
      else
      {
         /* both variables have mixed sign (xl < 0 && xu > 0 && yl < 0 && yu > 0) and both xl*yl and xu*yu are feasible
          * cannot generate cut for this
          */
         return;
      }
   }
   else
   {
      if( xl >= 0.0 || yu <= 0.0 || SCIPisGT(scip, xl * yu, wu) )
      {
         xl = MAX(xl, 0.0);
         yu = MIN(yu, 0.0);
      }
      else if( xu <= 0.0 || yl >= 0.0 || SCIPisGT(scip, xu * yl, wu))
      {
         xu = MIN(xu, 0.0);
         yl = MAX(yl, 0.0);
      }
      else
      {
         /* both variables have mixed sign (xl < 0 && xu > 0 && yl < 0 && yu > 0) and both xl*yu and xu*yl are feasible
          * cannot generate cut for this
          */
         return;
      }
   }

   /* if x or y is fixed now or even infeasible, then do not think about a cut */
   if( SCIPisGE(scip, xl, xu) || SCIPisGE(scip, yl, yu) )
      return;

   /* reduce to positive orthant by flipping variables */
   if( xl < 0.0 )
   {
      flipx = TRUE;
      tmp = xu;
      xu = -xl;
      xl = -tmp;
      x0 = -x0;
   }
   else
      flipx = FALSE;

   if( yl < 0.0 )
   {
      flipy = TRUE;
      tmp = yu;
      yu = -yl;
      yl = -tmp;
      y0_ = -y0_;
   }
   else
      flipy = FALSE;

   if( flipx ^ flipy )
   {
      flipw = TRUE;
      tmp = wu;
      wu = -wl;
      wl = -tmp;
      w0 = -w0;
   }
   else
      flipw = FALSE;

   /* project refpoint into box not only for numerical reasons, but also due to preliminary bound tightening above */
   x0 = MIN(xu, MAX(x0, xl));
   y0_ = MIN(yu, MAX(y0_, yl));
   w0 = MIN(wu, MAX(w0, wl));

   SCIPdebugMessage("reduced points:\n");
   SCIPdebugMessage("x: %9g\t[%9g\t%9g]\n", x0, xl, xu);
   SCIPdebugMessage("y: %9g\t[%9g\t%9g]\n", y0_, yl, yu);
   SCIPdebugMessage("w: %9g\t[%9g\t%9g]\n", w0, wl, wu);

   if( SCIPisGE(scip, xl * yl, wl) && SCIPisLE(scip, xu * yu, wu) )
   {
      SCIPdebugMessage("box for x and y inside feasible region -> nothing to separate\n");
      return;
   }
   if( SCIPisGE(scip, x0 * y0_, w0) )
   {
      SCIPdebugMessage("point to separate not below curve -> cannot separate\n");
      return;
   }

   /* find intersections of halfline from origin
    * return if no proper point could be found
    */
   if( generateCutLTIfindIntersection(scip, 0.0, 0.0, x0, y0_, wl, wu, &xlow, &ylow, &xupp, &yupp) )
      return;

   SCIPdebugMessage("intersections:\n");
   SCIPdebugMessage("lower: %9g\t%9g\tprod %9g\n", xlow, ylow, xlow*ylow);
   SCIPdebugMessage("upper: %9g\t%9g\tprod %9g\n", xupp, yupp, xupp*yupp);

   /* Case 1: If both are outside of bounding box, either NW or SE, then McCormick is sufficient, so return */
   if( (xlow <= xl && yupp >= yu) || (ylow <= yl && xupp >= xu) )
      return;

   /* There will be at least one cut. Define coefficients and rhs ---will have to change them back if (flipX || flipY) */
   if( xlow >= xl && xupp <= xu && ylow >= yl && yupp <= yu )
   {
      /* Case 2: both are inside. Easy lifting... */
      if( generateCutLTIgenMulCoeff(scip, xlow, ylow, xupp, yupp, FALSE, cx, cy, cw) )
         return;

      c0x = *cx * xlow;
      c0y = *cy * ylow;
      c0w = *cw * wl;
   }
   else if( xlow >= xl && ylow >= yl && (xupp > xu || yupp > yu) )
   {
      /* Case 3a and 3b: through lower curve, but not upper. */
      if( yupp > yu )
      {
         /* upper intersect is North; place it within box */
         assert(!SCIPisInfinity(scip, yu));
         yupp = yu;
         xupp = wu / yu;
      }
      else
      {
         /* upper intersect is East; place it within box */
         assert(!SCIPisInfinity(scip, xu));
         xupp = xu;
         yupp = wu / xu;
      }

      /* find intersection on low curve on half line through new point and (x0,y0_) */
      if( generateCutLTIfindIntersection(scip, xupp, yupp, x0, y0_, wl, SCIP_INVALID, &xlow, &ylow, NULL, NULL) )
         return;

      /* check whether McCormick is sufficient */
      if( xlow < xl || ylow < yl )
         return;

      /* lift inequality on lower point */
      if( generateCutLTIgenMulCoeff(scip, xlow, ylow, xupp, yupp, FALSE, cx, cy, cw) )
         return;

      c0x = *cx * xlow;
      c0y = *cy * ylow;
      c0w = *cw * wl;
   }
   else if( xupp <= xu && yupp <= yu && (xlow < xl || ylow < yl) )
   {
      /* Case 4a and 4b: viceversa (lift for validity) */
      if( ylow < yl )
      {
         /* upper intersect is South; place it within box */
         assert(!SCIPisZero(scip, yl));
         ylow = yl;
         xlow = wl / yl;
      }
      else
      {
         /* upper intersect is West; place it within box */
         assert(!SCIPisZero(scip, xl));
         xlow = xl;
         ylow = wl / xl;
      }

      /* find intersection on low curve on half line through new point and (x0,y0) */
      if( generateCutLTIfindIntersection(scip, xlow, ylow, x0, y0_, SCIP_INVALID, wu, NULL, NULL, &xupp, &yupp) )
         return;

      /* check whether McCormick is sufficient */
      if( xupp > xu || yupp > yu )
         return;

      /* lift inequality on UPPER point */
      if( generateCutLTIgenMulCoeff(scip, xlow, ylow, xupp, yupp, TRUE, cx, cy, cw) )
         return;

      c0x = *cx * xupp;
      c0y = *cy * yupp;
      c0w = *cw * wu;
   }
   else if( (xlow < xl && xupp > xu) || (ylow < yl && yupp > yu) )
   {
      /* Case 5: both outside of bounding box, N and S or W and E. */
#if 0
      SCIP_Real xlow2;
      SCIP_Real ylow2;
      SCIP_Real xupp2;
      SCIP_Real yupp2;
#endif

      if( ylow < yl )
      {
         /* upper intersect is South; place it within box */
         assert(!SCIPisZero(scip, yl));
         assert(!SCIPisZero(scip, yu));
         ylow = yl;
         yupp = yu;
         xlow = wl / yl;
         xupp = wu / yu;
      }
      else
      {
         /* upper intersect is West; place it within box */
         assert(!SCIPisZero(scip, xl));
         assert(!SCIPisZero(scip, xu));
         xlow = xl;
         xupp = xu;
         ylow = wl / xl;
         yupp = wu / xu;
      }

      SCIPdebugMessage("New intersections:\n");
      SCIPdebugMessage("lower: %9g\t%9g\tprod %9g\n", xlow, ylow, xlow*ylow);
      SCIPdebugMessage("upper: %9g\t%9g\tprod %9g\n", xupp, yupp, xupp*yupp);

#if 1
      /* Nothing to find. Just separate two inequalities at the same point, just using different support */
      if( generateCutLTIgenMulCoeff(scip, xlow, ylow, xupp, yupp, FALSE, cx, cy, cw) )
      {
         if( generateCutLTIgenMulCoeff(scip, xlow, ylow, xupp, yupp, TRUE, cx, cy, cw) )
            return;

         c0x = *cx * xupp;
         c0y = *cy * yupp;
         c0w = *cw * wu;
      }
      else
      {
         c0x = *cx * xlow;
         c0y = *cy * ylow;
         c0w = *cw * wl;
      }

#else
      /* find the intersection on the lower (upper) curve on the line through xLP and the upper (lower) point
       * this does not seem to work (cuts off solution at nous2), so it is disabled for now
       */
      if( generateCutLTIfindIntersection(scip, xlow, ylow, x0, y0_, SCIP_INVALID, wu, NULL, NULL, &xupp2, &yupp2) ||
         generateCutLTIgenMulCoeff(scip, xlow, ylow, xupp2, yupp2, FALSE, cx, cx, cw) )
      {
         if( generateCutLTIfindIntersection(scip, xupp, yupp, x0, y0_, wl, SCIP_INVALID, &xlow2, &ylow2, NULL, NULL) ||
            generateCutLTIgenMulCoeff(scip, xlow2, ylow2, xupp, yupp, TRUE, cx, cy, cw) )
            return;

         c0x = *cx * xupp;
         c0y = *cy * yupp;
         c0w = *cw * wu;
      }
      else
      {
         c0x = *cx * xlow;
         c0y = *cy * ylow;
         c0w = *cw * wl;
      }
#endif
   }
   else
   {
      SCIPdebugMessage("points are in a weird position:\n");
      SCIPdebugMessage("lower: %9g\t%9g\tprod %9g\n", xlow, ylow, xlow*ylow);
      SCIPdebugMessage("upper: %9g\t%9g\tprod %9g\n", xupp, yupp, xupp*yupp);

      return;
   }

   SCIPdebugMessage("cut w.r.t. reduced points: %gx-%g %+gy-%g %+gw-%g >= 0\n",
      *cx, c0x, *cy, c0y, *cw, c0w);

   /* re-transform back into original variables */
   if( flipx )
      *cx = -*cx;
   if( flipy )
      *cy = -*cy;
   if( flipw )
      *cw = -*cw;

   *c0 = c0x + c0y + c0w;

   *success = TRUE;
}

/** tries to generate a cut if constraint quadratic function is factorable and there are linear variables
 * computes what is called a lifted tangent inequality described in
 *   Belotti, Miller, Namazifar, Lifted inequalities for bounded products of variables, SIAG/OPT Views-and-News 22:1, 2011
 */
static
SCIP_RETCODE generateCutLTI(
   SCIP*                 scip,               /**< SCIP data structure */
   SCIP_CONS*            cons,               /**< constraint */
   SCIP_SIDETYPE         violside,           /**< for which side a cut should be generated */
   SCIP_Real*            ref,                /**< reference solution where to generate the cut */
   SCIP_SOL*             sol,                /**< solution that shall be cutoff, NULL for LP solution */
   SCIP_Real**           cutcoeflin,         /**< buffer to store pointer to array with coefficients for linear variables */
   SCIP_Real*            cutcoefquad,        /**< array to store cut coefficients for quadratic variables */
   SCIP_Real*            cutlhs,             /**< buffer to store cut lhs */
   SCIP_Real*            cutrhs,             /**< buffer to store cut rhs */
   SCIP_Bool*            islocal,            /**< buffer to set to TRUE if local information was used */
   SCIP_Bool*            success,            /**< buffer to indicate whether a cut was successfully computed */
   char*                 name                /**< buffer to store name of cut */
   )
{
   SCIP_CONSDATA* consdata;
   SCIP_Real leftminactivity;
   SCIP_Real leftmaxactivity;
   SCIP_Real leftrefactivity;
   SCIP_Real rightminactivity;
   SCIP_Real rightmaxactivity;
   SCIP_Real rightrefactivity;
   SCIP_Real rhsminactivity;
   SCIP_Real rhsmaxactivity;
   SCIP_Real rhsrefactivity;
   SCIP_Real coefleft;
   SCIP_Real coefright;
   SCIP_Real coefrhs;
   int i;

   assert(scip != NULL);
   assert(cons != NULL);
   assert(ref  != NULL);
   assert(cutcoeflin != NULL);
   assert(cutcoefquad != NULL);
   assert(cutlhs  != NULL);
   assert(cutrhs  != NULL);
   assert(islocal != NULL);
   assert(success != NULL);
   assert(name != NULL);
   /* currently only separate LP solution or solutions given as SCIP_SOL, i.e., no cutgeneration during initlp */
   assert(sol != NULL || SCIPgetLPSolstat(scip) == SCIP_LPSOLSTAT_OPTIMAL);

   consdata = SCIPconsGetData(cons);
   assert(consdata != NULL);
   assert(consdata->nlinvars > 0);
   assert(consdata->factorleft != NULL);
   assert(consdata->factorright != NULL);

   *success = FALSE;
   *cutlhs = -SCIPinfinity(scip); /* for compiler */

   /* write violated constraints as factorleft * factorright '==' rhs
    * where rhs are constraint sides - activity bound of linear part
    */
   rhsminactivity = consdata->lhs;
   rhsmaxactivity = consdata->rhs;
   rhsrefactivity = (violside == SCIP_SIDETYPE_LEFT ? consdata->lhs : consdata->rhs);

   for( i = 0; i < consdata->nlinvars; ++i )
   {
      if( !SCIPisInfinity(scip, -rhsminactivity) )
      {
         if( consdata->lincoefs[i] < 0.0 )
         {
            if( SCIPisInfinity(scip, -SCIPvarGetLbLocal(consdata->linvars[i])) )
               rhsminactivity = -SCIPinfinity(scip);
            else
               rhsminactivity -= consdata->lincoefs[i] * SCIPvarGetLbLocal(consdata->linvars[i]);
         }
         else
         {
            assert(consdata->lincoefs[i] > 0.0);
            if( SCIPisInfinity(scip, SCIPvarGetUbLocal(consdata->linvars[i])) )
               rhsminactivity = -SCIPinfinity(scip);
            else
               rhsminactivity -= consdata->lincoefs[i] * SCIPvarGetUbLocal(consdata->linvars[i]);
         }
      }
      if( !SCIPisInfinity(scip, rhsmaxactivity) )
      {
         if( consdata->lincoefs[i] < 0.0 )
         {
            if( SCIPisInfinity(scip, SCIPvarGetUbLocal(consdata->linvars[i])) )
               rhsmaxactivity = SCIPinfinity(scip);
            else
               rhsmaxactivity -= consdata->lincoefs[i] * SCIPvarGetUbLocal(consdata->linvars[i]);
         }
         else
         {
            assert(consdata->lincoefs[i] > 0.0);
            if( SCIPisInfinity(scip, -SCIPvarGetLbLocal(consdata->linvars[i])) )
               rhsmaxactivity = SCIPinfinity(scip);
            else
               rhsmaxactivity -= consdata->lincoefs[i] * SCIPvarGetLbLocal(consdata->linvars[i]);
         }
      }
      rhsrefactivity -= consdata->lincoefs[i] * SCIPgetSolVal(scip, sol, consdata->linvars[i]);
   }

   if( SCIPisInfinity(scip, -rhsminactivity) || SCIPisInfinity(scip, rhsmaxactivity) )
   {
      /* if right hand side is unbounded, then cannot do LTI */
      return SCIP_OKAY;
   }

   if( !SCIPisFeasPositive(scip, rhsminactivity) && !SCIPisFeasNegative(scip, rhsmaxactivity) )
   {
      /* if right hand side has 0 inside activity, then cannot do anything
       * if it has 0.0 as min or max activity, then a usual McCormick should be sufficient, too
       */
      return SCIP_OKAY;
   }

   leftminactivity = consdata->factorleft[consdata->nquadvars];
   leftmaxactivity = consdata->factorleft[consdata->nquadvars];
   leftrefactivity = consdata->factorleft[consdata->nquadvars];
   rightminactivity = consdata->factorright[consdata->nquadvars];
   rightmaxactivity = consdata->factorright[consdata->nquadvars];
   rightrefactivity = consdata->factorright[consdata->nquadvars];
   for( i = 0; i < consdata->nquadvars; ++i )
   {
      if( !SCIPisInfinity(scip, -leftminactivity) )
      {
         if( consdata->factorleft[i] > 0.0 )
         {
            if( SCIPisInfinity(scip, -SCIPvarGetLbLocal(consdata->quadvarterms[i].var)) )
               leftminactivity = -SCIPinfinity(scip);
            else
               leftminactivity += consdata->factorleft[i] * SCIPvarGetLbLocal(consdata->quadvarterms[i].var);
         }
         else if( consdata->factorleft[i] < 0.0 )
         {
            if( SCIPisInfinity(scip, SCIPvarGetUbLocal(consdata->quadvarterms[i].var)) )
               leftminactivity = -SCIPinfinity(scip);
            else
               leftminactivity += consdata->factorleft[i] * SCIPvarGetUbLocal(consdata->quadvarterms[i].var);
         }
      }
      if( !SCIPisInfinity(scip, leftmaxactivity) )
      {
         if( consdata->factorleft[i] > 0.0 )
         {
            if( SCIPisInfinity(scip, SCIPvarGetUbLocal(consdata->quadvarterms[i].var)) )
               leftmaxactivity = SCIPinfinity(scip);
            else
               leftmaxactivity += consdata->factorleft[i] * SCIPvarGetUbLocal(consdata->quadvarterms[i].var);
         }
         else if( consdata->factorleft[i] < 0.0 )
         {
            if( SCIPisInfinity(scip, -SCIPvarGetLbLocal(consdata->quadvarterms[i].var)) )
               leftmaxactivity = SCIPinfinity(scip);
            else
               leftmaxactivity += consdata->factorleft[i] * SCIPvarGetLbLocal(consdata->quadvarterms[i].var);
         }
      }
      leftrefactivity += consdata->factorleft[i] * ref[i];

      if( !SCIPisInfinity(scip, -rightminactivity) )
      {
         if( consdata->factorright[i] > 0.0 )
         {
            if( SCIPisInfinity(scip, -SCIPvarGetLbLocal(consdata->quadvarterms[i].var)) )
               rightminactivity = -SCIPinfinity(scip);
            else
               rightminactivity += consdata->factorright[i] * SCIPvarGetLbLocal(consdata->quadvarterms[i].var);
         }
         else if( consdata->factorright[i] < 0.0 )
         {
            if( SCIPisInfinity(scip, SCIPvarGetUbLocal(consdata->quadvarterms[i].var)) )
               rightminactivity = -SCIPinfinity(scip);
            else
               rightminactivity += consdata->factorright[i] * SCIPvarGetUbLocal(consdata->quadvarterms[i].var);
         }
      }
      if( !SCIPisInfinity(scip, rightmaxactivity) )
      {
         if( consdata->factorright[i] > 0.0 )
         {
            if( SCIPisInfinity(scip, SCIPvarGetUbLocal(consdata->quadvarterms[i].var)) )
               rightmaxactivity = SCIPinfinity(scip);
            else
               rightmaxactivity += consdata->factorright[i] * SCIPvarGetUbLocal(consdata->quadvarterms[i].var);
         }
         else if( consdata->factorright[i] < 0.0 )
         {
            if( SCIPisInfinity(scip, -SCIPvarGetLbLocal(consdata->quadvarterms[i].var)) )
               rightmaxactivity = SCIPinfinity(scip);
            else
               rightmaxactivity += consdata->factorright[i] * SCIPvarGetLbLocal(consdata->quadvarterms[i].var);
         }
      }
      rightrefactivity += consdata->factorright[i] * ref[i];
   }

   /* if activities exceed "opposite" infinity, huge bounds seem to be involved, for which the below method is not prepared */
   if( SCIPisInfinity(scip, leftminactivity)  || SCIPisInfinity(scip, -leftmaxactivity) ||
       SCIPisInfinity(scip, rightminactivity) || SCIPisInfinity(scip, -rightmaxactivity) )
      return SCIP_OKAY;

   /* if any of the factors is essentially fixed, give up and do usual method (numerically less sensitive, I hope) */
   if( SCIPisRelEQ(scip, leftminactivity, leftmaxactivity) || SCIPisRelEQ(scip, rightminactivity, rightmaxactivity) )
      return SCIP_OKAY;

   /* success can only be expected for separation of violated x*y <= w, assuming x>=0, y>=0
    * @todo we should check this early? */

   /* call Couenne magic */
   generateCutLTIcomputeCoefs(scip,
      leftminactivity, leftmaxactivity, leftrefactivity,
      rightminactivity, rightmaxactivity, rightrefactivity,
      rhsminactivity, rhsmaxactivity, rhsrefactivity,
      &coefleft, &coefright, &coefrhs, cutlhs,
      success);

   if( !*success )
      return SCIP_OKAY;

   SCIPdebugMessage("LTI for x[%g,%g] * y[%g,%g] = w[%g,%g]: %gx %+gy %+gw >= %g;  feas: %g\n",
      leftminactivity, leftmaxactivity, rightminactivity, rightmaxactivity, rhsminactivity, rhsmaxactivity,
      coefleft, coefright, coefrhs, *cutlhs,
      coefleft * leftrefactivity + coefright * rightrefactivity + coefrhs * rhsrefactivity - *cutlhs
      );

   if( coefleft * leftrefactivity + coefright * rightrefactivity + coefrhs * rhsrefactivity >= *cutlhs )
   {
      SCIPdebugMessage("does not cutoff point? :-(\n");
      *success = FALSE;
      return SCIP_OKAY;
   }

   /* setup cut coefs for
    *   coefleft * leftfactor + coefright * rightfactor + coefrhs * w >= cutlhs, where conslhs - lincoefs <= w <= consrhs - lincoefs
    */
   for( i = 0; i < consdata->nquadvars; ++i )
      cutcoefquad[i] = coefleft * consdata->factorleft[i] + coefright * consdata->factorright[i];
   assert(i == consdata->nquadvars);
   *cutlhs -= coefleft * consdata->factorleft[i] + coefright * consdata->factorright[i];

   SCIP_CALL( SCIPallocBufferArray(scip, cutcoeflin, consdata->nlinvars) );
   for( i = 0; i < consdata->nlinvars; ++i )
      (*cutcoeflin)[i] = -coefrhs * consdata->lincoefs[i];
   if( coefrhs > 0.0 )
   {
      /* use coefrhs * w <= coefrhs * (consrhs - lincoefs) */
      assert(!SCIPisInfinity(scip, consdata->rhs));
      *cutlhs -= coefrhs * consdata->rhs;
   }
   else
   {
      /* use coefrhs * w <= coeflhs * (conslhs - lincoefs) */
      assert(!SCIPisInfinity(scip, -consdata->lhs));
      *cutlhs -= coefrhs * consdata->lhs;
   }

   *cutrhs = SCIPinfinity(scip);
   *islocal = TRUE;

   (void) SCIPsnprintf(name, SCIP_MAXSTRLEN, "%s_lti_%d", SCIPconsGetName(cons), SCIPgetNLPs(scip));

   *success = TRUE;

   return SCIP_OKAY;
}

/** computes coefficients of linearization of a square term in a reference point */
static
void addSquareLinearization(
   SCIP*                 scip,               /**< SCIP data structure */
   SCIP_Real             sqrcoef,            /**< coefficient of square term */
   SCIP_Real             refpoint,           /**< point where to linearize */
   SCIP_Bool             isint,              /**< whether corresponding variable is a discrete variable, and thus linearization could be moved */
   SCIP_Real*            lincoef,            /**< buffer to add coefficient of linearization */
   SCIP_Real*            linconstant,        /**< buffer to add constant of linearization */
   SCIP_Bool*            success             /**< buffer to set to FALSE if linearization has failed due to large numbers */
   )
{
   assert(scip != NULL);
   assert(lincoef != NULL);
   assert(linconstant != NULL);
   assert(success != NULL);

   if( sqrcoef == 0.0 )
      return;

   if( SCIPisInfinity(scip, REALABS(refpoint)) )
   {
      *success = FALSE;
      return;
   }

   if( !isint || SCIPisIntegral(scip, refpoint) )
   {
      SCIP_Real tmp;

      /* sqrcoef * x^2  ->  tangent in refpoint = sqrcoef * 2 * refpoint * (x - refpoint) */

      tmp = sqrcoef * refpoint;

      if( SCIPisInfinity(scip, 2.0 * REALABS(tmp)) )
      {
         *success = FALSE;
         return;
      }

      *lincoef += 2.0 * tmp;
      tmp *= refpoint;
      *linconstant -= tmp;
   }
   else
   {
      /* sqrcoef * x^2 ->  secant between f=floor(refpoint) and f+1 = sqrcoef * (f^2 + ((f+1)^2 - f^2) * (x-f)) = sqrcoef * (-f*(f+1) + (2*f+1)*x) */
      SCIP_Real f;
      SCIP_Real coef;
      SCIP_Real constant;

      f = SCIPfloor(scip, refpoint);

      coef     =  sqrcoef * (2.0 * f + 1.0);
      constant = -sqrcoef * f * (f + 1.0);

      if( SCIPisInfinity(scip, REALABS(coef)) || SCIPisInfinity(scip, REALABS(constant)) )
      {
         *success = FALSE;
         return;
      }

      *lincoef     += coef;
      *linconstant += constant;
   }
}

/** computes coefficients of secant of a square term */
static
void addSquareSecant(
   SCIP*                 scip,               /**< SCIP data structure */
   SCIP_Real             sqrcoef,            /**< coefficient of square term */
   SCIP_Real             lb,                 /**< lower bound on variable */
   SCIP_Real             ub,                 /**< upper bound on variable */
   SCIP_Real             refpoint,           /**< point for which to compute value of linearization */
   SCIP_Real*            lincoef,            /**< buffer to add coefficient of secant */
   SCIP_Real*            linconstant,        /**< buffer to add constant of secant */
   SCIP_Bool*            success             /**< buffer to set to FALSE if secant has failed due to large numbers or unboundedness */
   )
{
   SCIP_Real coef;
   SCIP_Real constant;

   assert(scip != NULL);
   assert(!SCIPisInfinity(scip,  lb));
   assert(!SCIPisInfinity(scip, -ub));
   assert(SCIPisLE(scip, lb, ub));
   assert(SCIPisLE(scip, lb, refpoint));
   assert(SCIPisGE(scip, ub, refpoint));
   assert(lincoef != NULL);
   assert(linconstant != NULL);
   assert(success != NULL);

   if( sqrcoef == 0.0 )
      return;

   if( SCIPisInfinity(scip, -lb) || SCIPisInfinity(scip, ub) )
   {
      /* unboundedness */
      *success = FALSE;
      return;
   }

   /* sqrcoef * x^2 -> sqrcoef * (lb * lb + (ub*ub - lb*lb)/(ub-lb) * (x-lb)) = sqrcoef * (lb*lb + (ub+lb)*(x-lb)) = sqrcoef * ((lb+ub)*x - lb*ub) */

   coef     =  sqrcoef * (lb + ub);
   constant = -sqrcoef * lb * ub;
   if( SCIPisInfinity(scip, REALABS(coef)) || SCIPisInfinity(scip, REALABS(constant)) )
   {
      *success = FALSE;
      return;
   }

   *lincoef     += coef;
   *linconstant += constant;
}

/** computes coefficients of linearization of a bilinear term in a reference point */
static
void addBilinLinearization(
   SCIP*                 scip,               /**< SCIP data structure */
   SCIP_Real             bilincoef,          /**< coefficient of bilinear term */
   SCIP_Real             refpointx,          /**< point where to linearize first  variable */
   SCIP_Real             refpointy,          /**< point where to linearize second variable */
   SCIP_Real*            lincoefx,           /**< buffer to add coefficient of first  variable in linearization */
   SCIP_Real*            lincoefy,           /**< buffer to add coefficient of second variable in linearization */
   SCIP_Real*            linconstant,        /**< buffer to add constant of linearization */
   SCIP_Bool*            success             /**< buffer to set to FALSE if linearization has failed due to large numbers */
   )
{
   SCIP_Real constant;

   assert(scip != NULL);
   assert(lincoefx != NULL);
   assert(lincoefy != NULL);
   assert(linconstant != NULL);
   assert(success != NULL);

   if( bilincoef == 0.0 )
      return;

   if( SCIPisInfinity(scip, REALABS(refpointx)) || SCIPisInfinity(scip, REALABS(refpointy)) )
   {
      *success = FALSE;
      return;
   }

   /* bilincoef * x * y ->  bilincoef * (refpointx * refpointy + refpointy * (x - refpointx) + refpointx * (y - refpointy))
    *                    = -bilincoef * refpointx * refpointy + bilincoef * refpointy * x + bilincoef * refpointx * y
    */

   constant = -bilincoef * refpointx * refpointy;

   if( SCIPisInfinity(scip, REALABS(bilincoef * refpointx)) || SCIPisInfinity(scip, REALABS(bilincoef * refpointy)) || SCIPisInfinity(scip, REALABS(constant)) )
   {
      *success = FALSE;
      return;
   }

   *lincoefx    += bilincoef * refpointy;
   *lincoefy    += bilincoef * refpointx;
   *linconstant += constant;
}

/** computes coefficients of McCormick under- or overestimation of a bilinear term */
static
void addBilinMcCormick(
   SCIP*                 scip,               /**< SCIP data structure */
   SCIP_Real             bilincoef,          /**< coefficient of bilinear term */
   SCIP_Real             lbx,                /**< lower bound on first variable */
   SCIP_Real             ubx,                /**< upper bound on first variable */
   SCIP_Real             refpointx,          /**< reference point for first variable */
   SCIP_Real             lby,                /**< lower bound on second variable */
   SCIP_Real             uby,                /**< upper bound on second variable */
   SCIP_Real             refpointy,          /**< reference point for second variable */
   SCIP_Bool             overestimate,       /**< whether to compute an overestimator instead of an underestimator */
   SCIP_Real*            lincoefx,           /**< buffer to add coefficient of first  variable in linearization */
   SCIP_Real*            lincoefy,           /**< buffer to add coefficient of second variable in linearization */
   SCIP_Real*            linconstant,        /**< buffer to add constant of linearization */
   SCIP_Bool*            success             /**< buffer to set to FALSE if linearization has failed due to large numbers */
   )
{
   SCIP_Real constant;
   SCIP_Real coefx;
   SCIP_Real coefy;

   assert(scip != NULL);
   assert(!SCIPisInfinity(scip,  lbx));
   assert(!SCIPisInfinity(scip, -ubx));
   assert(!SCIPisInfinity(scip,  lby));
   assert(!SCIPisInfinity(scip, -uby));
   assert(SCIPisLE(scip, lbx, ubx));
   assert(SCIPisLE(scip, lby, uby));
   assert(SCIPisLE(scip, lbx, refpointx));
   assert(SCIPisGE(scip, ubx, refpointx));
   assert(SCIPisLE(scip, lby, refpointy));
   assert(SCIPisGE(scip, uby, refpointy));
   assert(lincoefx != NULL);
   assert(lincoefy != NULL);
   assert(linconstant != NULL);
   assert(success != NULL);

   if( bilincoef == 0.0 )
      return;

   if( overestimate )
      bilincoef = -bilincoef;

   if( SCIPisRelEQ(scip, lbx, ubx) && SCIPisRelEQ(scip, lby, uby) )
   {
      /* both x and y are mostly fixed */
      SCIP_Real cand1;
      SCIP_Real cand2;
      SCIP_Real cand3;
      SCIP_Real cand4;

      coefx = 0.0;
      coefy = 0.0;

      /* estimate x * y by constant */
      cand1 = lbx * lby;
      cand2 = lbx * uby;
      cand3 = ubx * lby;
      cand4 = ubx * uby;

      if( bilincoef > 0.0 )
         constant = bilincoef * MAX( MAX(cand1, cand2), MAX(cand3, cand4) );
      else
         constant = bilincoef * MIN( MIN(cand1, cand2), MIN(cand3, cand4) );
   }
   else if( bilincoef > 0.0 )
   {
      /* either x or y is not fixed and coef > 0.0 */
      if( !SCIPisInfinity(scip, -lbx) && !SCIPisInfinity(scip, -lby) &&
         (SCIPisInfinity(scip,  ubx) || SCIPisInfinity(scip,  uby) || (uby - refpointy) * (ubx - refpointx) >= (refpointy - lby) * (refpointx - lbx)) )
      {
         if( SCIPisRelEQ(scip, lbx, ubx) )
         {
            /* x*y = lbx * y + (x-lbx) * y >= lbx * y + (x-lbx) * lby >= lbx * y + min{(ubx-lbx) * lby, 0 * lby} */
            coefx    =  0.0;
            coefy    =  bilincoef * lbx;
            constant =  bilincoef * (lby < 0.0 ? (ubx-lbx) * lby : 0.0);
         }
         else if( SCIPisRelEQ(scip, lby, uby) )
         {
            /* x*y = lby * x + (y-lby) * x >= lby * x + (y-lby) * lbx >= lby * x + min{(uby-lby) * lbx, 0 * lbx} */
            coefx    =  bilincoef * lby;
            coefy    =  0.0;
            constant =  bilincoef * (lbx < 0.0 ? (uby-lby) * lbx : 0.0);
         }
         else
         {
            coefx    =  bilincoef * lby;
            coefy    =  bilincoef * lbx;
            constant = -bilincoef * lbx * lby;
         }
      }
      else if( !SCIPisInfinity(scip, ubx) && !SCIPisInfinity(scip, uby) )
      {
         if( SCIPisRelEQ(scip, lbx, ubx) )
         {
            /* x*y = ubx * y + (x-ubx) * y >= ubx * y + (x-ubx) * uby >= ubx * y + min{(lbx-ubx) * uby, 0 * uby} */
            coefx    =  0.0;
            coefy    =  bilincoef * ubx;
            constant =  bilincoef * (uby > 0.0 ? (lbx-ubx) * uby : 0.0);
         }
         else if( SCIPisRelEQ(scip, lby, uby) )
         {
            /* x*y = uby * x + (y-uby) * x >= uby * x + (y-uby) * ubx >= uby * x + min{(lby-uby) * ubx, 0 * ubx} */
            coefx    =  bilincoef * uby;
            coefy    =  0.0;
            constant =  bilincoef * (ubx > 0.0 ? (lby-uby) * ubx : 0.0);
         }
         else
         {
            coefx    =  bilincoef * uby;
            coefy    =  bilincoef * ubx;
            constant = -bilincoef * ubx * uby;
         }
      }
      else
      {
         *success = FALSE;
         return;
      }
   }
   else
   {
      /* either x or y is not fixed and coef < 0.0 */
      if( !SCIPisInfinity(scip,  ubx) && !SCIPisInfinity(scip, -lby) &&
         (SCIPisInfinity(scip, -lbx) || SCIPisInfinity(scip,  uby) || (ubx - lbx) * (refpointy - lby) <= (uby - lby) * (refpointx - lbx)) )
      {
         if( SCIPisRelEQ(scip, lbx, ubx) )
         {
            /* x*y = ubx * y + (x-ubx) * y <= ubx * y + (x-ubx) * lby <= ubx * y + max{(lbx-ubx) * lby, 0 * lby} */
            coefx    =  0.0;
            coefy    =  bilincoef * ubx;
            constant =  bilincoef * (lby < 0.0 ? (lbx - ubx) * lby : 0.0);
         }
         else if( SCIPisRelEQ(scip, lby, uby) )
         {
            /* x*y = lby * x + (y-lby) * x <= lby * x + (y-lby) * ubx <= lby * x + max{(uby-lby) * ubx, 0 * ubx} */
            coefx    =  bilincoef * lby;
            coefy    =  0.0;
            constant =  bilincoef * (ubx > 0.0 ? (uby - lby) * ubx : 0.0);
         }
         else
         {
            coefx    =  bilincoef * lby;
            coefy    =  bilincoef * ubx;
            constant = -bilincoef * ubx * lby;
         }
      }
      else if( !SCIPisInfinity(scip, -lbx) && !SCIPisInfinity(scip, uby) )
      {
         if( SCIPisRelEQ(scip, lbx, ubx) )
         {
            /* x*y = lbx * y + (x-lbx) * y <= lbx * y + (x-lbx) * uby <= lbx * y + max{(ubx-lbx) * uby, 0 * uby} */
            coefx    =  0.0;
            coefy    =  bilincoef * lbx;
            constant =  bilincoef * (uby > 0.0 ? (ubx-lbx) * uby : 0.0);
         }
         else if( SCIPisRelEQ(scip, lby, uby) )
         {
            /* x*y = uby * x + (y-uby) * x <= uby * x + (y-uby) * lbx <= uby * x + max{(lby-uby) * lbx, 0 * lbx} */
            coefx    =  bilincoef * uby;
            coefy    =  0.0;
            constant =  bilincoef * (lbx < 0.0 ? (lby-uby) * lbx : 0.0);
         }
         else
         {
            coefx    =  bilincoef * uby;
            coefy    =  bilincoef * lbx;
            constant = -bilincoef * lbx * uby;
         }
      }
      else
      {
         *success = FALSE;
         return;
      }
   }

   if( SCIPisInfinity(scip, REALABS(coefx)) || SCIPisInfinity(scip, REALABS(coefy)) || SCIPisInfinity(scip, REALABS(constant)) )
   {
      *success = FALSE;
      return;
   }

   if( overestimate )
   {
      coefx    = -coefx;
      coefy    = -coefy;
      constant = -constant;
   }

   /* SCIPdebugMessage("%.20g * x[%.20g,%.20g] * y[%.20g,%.20g] %c= %.20g * x %+.20g * y %+.20g\n", bilincoef, lbx, ubx, lby, uby, overestimate ? '<' : '>', coefx, coefy, constant); */

   *lincoefx    += coefx;
   *lincoefy    += coefy;
   *linconstant += constant;
}

/** computes cut coefficients by linearizing a quadratic function */
static
SCIP_RETCODE generateCutConvex(
   SCIP*                 scip,               /**< SCIP data structure */
   SCIP_CONS*            cons,               /**< constraint */
   SCIP_SIDETYPE         violside,           /**< side for which to generate cut */
   SCIP_Real*            ref,                /**< reference solution where to generate the cut */
   SCIP_Real*            coef,               /**< array to store cut coefficients w.r.t. quadratic variables */
   SCIP_Real*            lhs,                /**< buffer to store left-hand-side of cut */
   SCIP_Real*            rhs,                /**< buffer to store right-hand-side of cut */
   SCIP_Bool*            islocal,            /**< buffer to set to TRUE if local bounds were used */
   SCIP_Bool*            success,            /**< buffer to indicate whether a cut was successfully computed */
   char*                 name                /**< buffer to store name for cut */
   )
{
   SCIP_CONSDATA* consdata;
   SCIP_BILINTERM* bilinterm;
   SCIP_Real constant;
   SCIP_VAR* var;
   int var2pos;
   int j;
   int k;

   assert(scip != NULL);
   assert(cons != NULL);
   assert(ref  != NULL);
   assert(coef != NULL);
   assert(lhs  != NULL);
   assert(rhs  != NULL);
   assert(islocal != NULL);
   assert(success != NULL);

   consdata = SCIPconsGetData(cons);
   assert(consdata != NULL);

   constant = 0.0;
   BMSclearMemoryArray(coef, consdata->nquadvars);
   *success = TRUE;

   /* do first-order Taylor for each term */
   for( j = 0; j < consdata->nquadvars && *success; ++j )
   {
      /* initialize coefficients to linear coefficients of quadratic variables */
      coef[j] += consdata->quadvarterms[j].lincoef;

      /* add linearization of square term */
      var = consdata->quadvarterms[j].var;
      addSquareLinearization(scip, consdata->quadvarterms[j].sqrcoef, ref[j], consdata->quadvarterms[j].nadjbilin == 0 && SCIPvarGetType(var) < SCIP_VARTYPE_CONTINUOUS, &coef[j], &constant, success);

      /* add linearization of bilinear terms that have var as first variable */
      for( k = 0; k < consdata->quadvarterms[j].nadjbilin && *success; ++k )
      {
         bilinterm = &consdata->bilinterms[consdata->quadvarterms[j].adjbilin[k]];
         if( bilinterm->var1 != var )
            continue;
         assert(bilinterm->var2 != var);
         assert(consdata->sepabilinvar2pos != NULL);

         var2pos = consdata->sepabilinvar2pos[consdata->quadvarterms[j].adjbilin[k]];
         assert(var2pos >= 0);
         assert(var2pos < consdata->nquadvars);
         assert(consdata->quadvarterms[var2pos].var == bilinterm->var2);

         addBilinLinearization(scip, bilinterm->coef, ref[j], ref[var2pos], &coef[j], &coef[var2pos], &constant, success);
      }
   }

   if( !*success )
   {
      SCIPdebugMessage("no success in linearization of <%s> in reference point\n", SCIPconsGetName(cons));
      return SCIP_OKAY;
   }

   if( violside == SCIP_SIDETYPE_LEFT )
   {
      *lhs = consdata->lhs - constant;
      *rhs = SCIPinfinity(scip);
   }
   else
   {
      *lhs = -SCIPinfinity(scip);
      *rhs = consdata->rhs - constant;
   }

   (void) SCIPsnprintf(name, SCIP_MAXSTRLEN, "%s_side%d_linearization_%d", SCIPconsGetName(cons), violside, SCIPgetNLPs(scip));

   return SCIP_OKAY;
}

/** computes cut coefficients for a nonconvex quadratic function */
static
SCIP_RETCODE generateCutNonConvex(
   SCIP*                 scip,               /**< SCIP data structure */
   SCIP_CONS*            cons,               /**< constraint */
   SCIP_SIDETYPE         violside,           /**< side for which to generate cut */
   SCIP_Real*            ref,                /**< reference solution where to generate the cut */
   SCIP_Real*            coef,               /**< array to store cut coefficients w.r.t. quadratic variables */
   SCIP_Real*            lhs,                /**< buffer to store left-hand-side of cut */
   SCIP_Real*            rhs,                /**< buffer to store right-hand-side of cut */
   SCIP_Bool*            islocal,            /**< buffer to set to TRUE if local bounds were used */
   SCIP_Bool*            success,            /**< buffer to indicate whether a cut was successfully computed */
   char*                 name                /**< buffer to store name for cut */
   )
{
   SCIP_CONSDATA* consdata;
   SCIP_BILINTERM* bilinterm;
   SCIP_Real constant;
   SCIP_Real sqrcoef;
   SCIP_VAR* var;
   int var2pos;
   int j;
   int k;

   assert(scip != NULL);
   assert(cons != NULL);
   assert(ref  != NULL);
   assert(coef != NULL);
   assert(lhs  != NULL);
   assert(rhs  != NULL);
   assert(islocal != NULL);
   assert(success != NULL);

   consdata = SCIPconsGetData(cons);
   assert(consdata != NULL);

   *islocal = TRUE;
   constant = 0.0;
   BMSclearMemoryArray(coef, consdata->nquadvars);
   *success = TRUE;

   /* underestimate (secant, McCormick) or linearize each term separately */
   for( j = 0; j < consdata->nquadvars && *success; ++j )
   {
      /* initialize coefficients to linear coefficients of quadratic variables */
      coef[j] += consdata->quadvarterms[j].lincoef;

      var = consdata->quadvarterms[j].var;

      sqrcoef = consdata->quadvarterms[j].sqrcoef;
      if( sqrcoef != 0.0 )
      {
         if( (violside == SCIP_SIDETYPE_LEFT  && sqrcoef <= 0.0) || (violside == SCIP_SIDETYPE_RIGHT && sqrcoef > 0.0) )
         {
            /* convex -> linearize */
            addSquareLinearization(scip, sqrcoef, ref[j], SCIPvarGetType(var) < SCIP_VARTYPE_CONTINUOUS, &coef[j], &constant, success);
         }
         else
         {
            /* not convex -> secant approximation */
            addSquareSecant(scip, sqrcoef, SCIPvarGetLbLocal(var), SCIPvarGetUbLocal(var), ref[j], &coef[j], &constant, success);
         }
      }

      for( k = 0; k < consdata->quadvarterms[j].nadjbilin && *success; ++k )
      {
         bilinterm = &consdata->bilinterms[consdata->quadvarterms[j].adjbilin[k]];
         if( bilinterm->var1 != var )
            continue;
         assert(bilinterm->var2 != var);
         assert(consdata->sepabilinvar2pos != NULL);

         var2pos = consdata->sepabilinvar2pos[consdata->quadvarterms[j].adjbilin[k]];
         assert(var2pos >= 0);
         assert(var2pos < consdata->nquadvars);
         assert(consdata->quadvarterms[var2pos].var == bilinterm->var2);

         addBilinMcCormick(scip, bilinterm->coef,
            SCIPvarGetLbLocal(var), SCIPvarGetUbLocal(var), ref[j],
            SCIPvarGetLbLocal(bilinterm->var2), SCIPvarGetUbLocal(bilinterm->var2), ref[var2pos],
            violside == SCIP_SIDETYPE_LEFT, &coef[j], &coef[var2pos], &constant, success);
      }
   }

   if( !*success )
   {
      SCIPdebugMessage("no success to find estimator for nonconvex <%s>\n", SCIPconsGetName(cons));
      return SCIP_OKAY;
   }

   if( violside == SCIP_SIDETYPE_LEFT )
   {
      *lhs = consdata->lhs - constant;
      *rhs = SCIPinfinity(scip);
   }
   else
   {
      *lhs = -SCIPinfinity(scip);
      *rhs = consdata->rhs - constant;
   }

   (void) SCIPsnprintf(name, SCIP_MAXSTRLEN, "%s_side%d_estimation_%d", SCIPconsGetName(cons), violside, SCIPgetNLPs(scip));

   return SCIP_OKAY;
}

/** generates a cut based on linearization (if convex) or McCormick (if nonconvex) in a given reference point */
static
SCIP_RETCODE generateCut(
   SCIP*                 scip,               /**< SCIP data structure */
   SCIP_CONSHDLR*        conshdlr,           /**< constraint handler */
   SCIP_CONS*            cons,               /**< constraint */
   SCIP_Real*            ref,                /**< reference solution where to generate the cut */
   SCIP_SOL*             sol,                /**< point that we aim to separate, or NULL for LP solution */
   SCIP_SIDETYPE         violside,           /**< for which side a cut should be generated */
   SCIP_ROW**            row,                /**< storage for cut */
   SCIP_Real*            efficacy,           /**< buffer to store efficacy of row in reference solution, or NULL if not of interest */
   SCIP_Bool             checkcurvmultivar,  /**< are we allowed to check the curvature of a multivariate quadratic function, if not done yet */
   SCIP_Real             minefficacy         /**< minimal required efficacy (violation scaled by maximal absolute coefficient) */
   )
{
   SCIP_CONSHDLRDATA* conshdlrdata;
   SCIP_CONSDATA* consdata;
   SCIP_Bool      islocal;
   char           cutname[SCIP_MAXSTRLEN];
   SCIP_Real*     lincoefs;
   SCIP_Real*     coef;
   SCIP_Real      lhs;
   SCIP_Real      rhs;
   SCIP_Bool      success;
   SCIP_Real      mincoef;
   SCIP_Real      maxcoef;
   SCIP_Real      lincoefsmax;
   SCIP_Real      lincoefsmin;
   SCIP_Real      viol;
   SCIP_Real      rowefficacy;
   SCIP_VAR*      var;
   int            j;

   assert(scip != NULL);
   assert(conshdlr != NULL);
   assert(cons != NULL);
   assert(ref != NULL);
   assert(row != NULL);

   conshdlrdata = SCIPconshdlrGetData(conshdlr);
   assert(conshdlrdata != NULL);

   consdata = SCIPconsGetData(cons);
   assert(consdata != NULL);
   assert(violside != SCIP_SIDETYPE_LEFT  || !SCIPisInfinity(scip, -consdata->lhs));
   assert(violside != SCIP_SIDETYPE_RIGHT || !SCIPisInfinity(scip,  consdata->rhs));

   *row = NULL;
   SCIP_CALL( SCIPallocBufferArray(scip, &coef, consdata->nquadvars) );
   lincoefs = consdata->lincoefs;
   lincoefsmax = consdata->lincoefsmax;
   lincoefsmin = consdata->lincoefsmin;
   islocal = SCIPconsIsLocal(cons);
   success = FALSE;
   lhs = -SCIPinfinity(scip);
   rhs = SCIPinfinity(scip);
   cutname[0] = '\0';

   /* if constraint function is factorable, then try to use factorable form to generate cut */
   if( consdata->factorleft != NULL )
   {
      if( consdata->nlinvars == 0 )
      {
         SCIP_CALL( generateCutFactorable(scip, cons, violside, ref, coef, &lhs, &rhs, &islocal, &success, cutname) );
      }
      else if( sol != NULL || SCIPgetLPSolstat(scip) == SCIP_LPSOLSTAT_OPTIMAL )
      {
         int i;

         /* generateCutLTI needs reference values also for the linear variables, which we only have if sol is given or LP has been solved */
         SCIP_CALL( generateCutLTI(scip, cons, violside, ref, sol, &lincoefs, coef, &lhs, &rhs, &islocal, &success, cutname) );

         /* in case of LTI cuts, we have to recompute the min and max of lincoefs, since they may have been modified */
         for( i = 0; i < consdata->nlinvars; ++i )
         {
            if( REALABS(lincoefs[i]) > lincoefsmax )
               lincoefsmax = REALABS(lincoefs[i]);
            if( REALABS(lincoefs[i]) < lincoefsmin )
               lincoefsmin = REALABS(lincoefs[i]);
         }
      }
   }

   /* if constraint is not factorable or failed to generate cut, try default method */
   if( !success )
   {
      SCIP_CALL( checkCurvature(scip, cons, checkcurvmultivar) );

      if( (violside == SCIP_SIDETYPE_LEFT && consdata->isconcave) || (violside == SCIP_SIDETYPE_RIGHT && consdata->isconvex) )
      {
         SCIP_CALL( generateCutConvex(scip, cons, violside, ref, coef, &lhs, &rhs, &islocal, &success, cutname) );
      }
      else
      {
         SCIP_CALL( generateCutNonConvex(scip, cons, violside, ref, coef, &lhs, &rhs, &islocal, &success, cutname) );
      }
   }

   /* cut should be one-sided, if any found */
   assert(!success || SCIPisInfinity(scip, -lhs) || SCIPisInfinity(scip, rhs));

   /* check if range of cut coefficients is ok
    * compute cut activity and violation in sol
    */
   mincoef = 0.0; /* only for lint */
   maxcoef = 0.0; /* only for compiler */
   viol = 0.0;    /* only for compiler */
   if( success )
   {
      SCIP_Real constant;
      SCIP_Real abscoef;
      SCIP_Real roundcoef;
      int       mincoefidx;
      SCIP_Real refactivity;
      SCIP_Real refactivitylinpart;

      /* compute activity of linear part in sol, if required
       * it is required if we need to check or return cut efficacy, for some debug output below, and some assert
       * round almost integral coefficients in integers, since this will happen when adding coefs to row (see comments below)
       */
      refactivitylinpart = 0.0;
#if !defined(SCIP_DEBUG)
      if( !SCIPisInfinity(scip, -minefficacy) || efficacy != NULL )
#endif
         for( j = 0; j < consdata->nlinvars; ++j )
            /* Loose variable have the best bound as LP solution value.
             * HOWEVER, they become column variables when they are added to a row (via SCIPaddVarsToRow below).
             * When this happens, their LP solution value changes to 0.0!
             * So when calculating the row activity, we treat loose variable as if they were already column variables.
             */
            if( SCIPvarGetStatus(consdata->linvars[j]) != SCIP_VARSTATUS_LOOSE )
               refactivitylinpart += (SCIPisIntegral(scip, lincoefs[j]) ? SCIPround(scip, lincoefs[j]) : lincoefs[j]) * SCIPgetSolVal(scip, sol, consdata->linvars[j]);

      assert(SCIPgetStage(scip) == SCIP_STAGE_SOLVING);

      constant = 0.0;
      do
      {
         refactivity = refactivitylinpart;
         mincoefidx = -1;
         mincoef = lincoefsmin;
         maxcoef = lincoefsmax;

         for( j = 0; j < consdata->nquadvars; ++j )
         {
            /* coefficients smaller than epsilon are rounded to 0.0 when added to row
             * further, coefficients very close to integral values are rounded to integers when added to LP
             * both cases can be problematic if variable value is very large (bad numerics)
             * thus, we anticipate by rounding coef here, but also modify constant so that cut is still valid (if possible)
             * i.e., estimate coef[i]*x by round(coef[i])*x + (coef[i]-round(coef[i])) * bound(x)
             * if required bound of x is not finite, then do nothing
             */
            roundcoef = SCIPround(scip, coef[j]);
            if( SCIPisEQ(scip, coef[j], roundcoef) && coef[j] != roundcoef ) /*lint !e777*/
            {
               SCIP_Real xbnd;

               var = consdata->quadvarterms[j].var;
               if( !SCIPisInfinity(scip, rhs) )
                  if( islocal )
                     xbnd = coef[j] > roundcoef ? SCIPvarGetLbLocal(var)  : SCIPvarGetUbLocal(var);
                  else
                     xbnd = coef[j] > roundcoef ? SCIPvarGetLbGlobal(var) : SCIPvarGetUbGlobal(var);
               else
                  if( islocal )
                     xbnd = coef[j] > roundcoef ? SCIPvarGetUbLocal(var)  : SCIPvarGetLbLocal(var);
                  else
                     xbnd = coef[j] > roundcoef ? SCIPvarGetUbGlobal(var) : SCIPvarGetLbGlobal(var);

               if( !SCIPisInfinity(scip, REALABS(xbnd)) )
               {
                  SCIPdebugMessage("var <%s> [%g,%g] has almost integral coef %.20g, round coefficient to %g and add constant %g\n",
                     SCIPvarGetName(var), SCIPvarGetLbGlobal(var), SCIPvarGetUbGlobal(var), coef[j], roundcoef, (coef[j]-roundcoef) * xbnd);
                  constant += (coef[j]-roundcoef) * xbnd;
                  coef[j] = roundcoef;
               }
            }

            if( coef[j] == 0.0 )
               continue;

            /* As above: When calculating the row activity, we treat loose variable as if they were already column variables. */
            if( SCIPvarGetStatus(consdata->quadvarterms[j].var) != SCIP_VARSTATUS_LOOSE )
               refactivity += coef[j] * SCIPgetSolVal(scip, sol, consdata->quadvarterms[j].var);

            abscoef = REALABS(coef[j]);
            if( abscoef < mincoef )
            {
               mincoef = abscoef;
               mincoefidx = j;
            }
            if( abscoef > maxcoef )
               maxcoef = abscoef;
         }

         if( maxcoef < mincoef )
         {
            /* if all coefficients are zero, then mincoef and maxcoef are still at their initial values
             * thus, skip cut generation if its boring
             */
            assert(maxcoef == 0.0);  /*lint !e777 */
            assert(mincoef == SCIPinfinity(scip));  /*lint !e777 */

            if( !SCIPisFeasPositive(scip, lhs) && !SCIPisFeasNegative(scip, rhs) )
            {
               SCIPdebugMessage("skip cut for constraint <%s> since all coefficients are zero and it's always satisfied\n", SCIPconsGetName(cons));
               success = FALSE;
            }
            else
            {
               /* cut will cutoff node */
            }

            break;
         }

         if( maxcoef / mincoef > conshdlrdata->cutmaxrange  )
         {
            SCIPdebugMessage("cut coefficients for constraint <%s> have very large range: mincoef = %g maxcoef = %g\n", SCIPconsGetName(cons), mincoef, maxcoef);
            if( mincoefidx >= 0 )
            {
               var = consdata->quadvarterms[mincoefidx].var;
               /* try to eliminate coefficient with minimal absolute value by weakening cut and try again
                * since we use local bounds, we need to make the row local if they are different from their global counterpart
                */
               if( ((coef[mincoefidx] > 0.0 && !SCIPisInfinity(scip, rhs)) || (coef[mincoefidx] < 0.0 && !SCIPisInfinity(scip, -lhs))) &&
                  !SCIPisInfinity(scip, -SCIPvarGetLbLocal(var)) )
               {
                  SCIPdebugMessage("eliminate coefficient %g for <%s> [%g, %g]\n", coef[mincoefidx], SCIPvarGetName(var), SCIPvarGetLbLocal(var), SCIPvarGetUbLocal(var));
                  constant += coef[mincoefidx] * SCIPvarGetLbLocal(var);
                  coef[mincoefidx] = 0.0;
                  islocal |= SCIPisGT(scip, SCIPvarGetLbLocal(var), SCIPvarGetLbGlobal(var));
                  continue;
               }
               else if( ((coef[mincoefidx] < 0.0 && !SCIPisInfinity(scip, rhs)) || (coef[mincoefidx] > 0.0 && !SCIPisInfinity(scip, -lhs))) &&
                  !SCIPisInfinity(scip, SCIPvarGetUbLocal(var)) )
               {
                  SCIPdebugMessage("eliminate coefficient %g for <%s> [%g, %g]\n", coef[mincoefidx], SCIPvarGetName(var), SCIPvarGetLbLocal(var), SCIPvarGetUbLocal(var));
                  constant += coef[mincoefidx] * SCIPvarGetUbLocal(var);
                  coef[mincoefidx] = 0.0;
                  islocal |= SCIPisLT(scip, SCIPvarGetUbLocal(var), SCIPvarGetUbGlobal(var));
                  continue;
               }
            }

            SCIPdebugMessage("skip cut\n");
            success = FALSE;
         }
         break;
      }
      while( TRUE );  /*lint !e506 */

      if( !SCIPisInfinity(scip, -lhs) )
      {
         lhs -= constant;
         viol = lhs - refactivity;
      }
      if( !SCIPisInfinity(scip,  rhs) )
      {
         rhs -= constant;
         viol = refactivity - rhs;
      }
   }

   if( success && SCIPisInfinity(scip, REALABS(lhs)) && SCIPisInfinity(scip, REALABS(rhs)) )
   {
      SCIPdebugMessage("skip cut for constraint <%s> because both sides are not finite: lhs = %g, rhs = %g\n", SCIPconsGetName(cons), lhs, rhs);
      success = FALSE;
   }

   /* check if reference point violates cut sufficiently */
   if( success )
   {
      rowefficacy = viol;
      switch( conshdlrdata->scaling )
      {
      case 'o' :
         break;

      case 'g' :
         /* in difference to SCIPgetCutEfficacy, we scale by norm only if the norm is > 1.0 this avoid finding cuts
          * efficient which are only very slightly violated CPLEX does not seem to scale row coefficients up too also we
          * use infinity norm, since that seem to be the usual scaling strategy in LP solvers (equilibrium scaling) */
         rowefficacy /= MAX(1.0, maxcoef);
         break;

      case 's' :
      {
         SCIP_Real abslhs = REALABS(lhs);

         if( !SCIPisInfinity(scip, abslhs) )
            rowefficacy /= MAX(1.0, abslhs);
         else
         {
            SCIP_Real absrhs = REALABS(rhs);

            rowefficacy /= MAX(1.0, absrhs);
         }

         break;
      }

      default:
         SCIPerrorMessage("Unknown scaling method '%c'.", conshdlrdata->scaling);
         SCIPABORT();
         return SCIP_INVALIDDATA;  /*lint !e527*/
      }
   }

   if( success && !SCIPisInfinity(scip, -minefficacy) && rowefficacy < minefficacy ) /*lint !e644*/
   {
      SCIPdebugMessage("skip cut for constraint <%s> because efficacy %g too low (< %g)\n", SCIPconsGetName(cons), rowefficacy, minefficacy);
      success = FALSE;
   }

   /* generate row */
   if( success )
   {
      SCIP_CALL( SCIPcreateEmptyRowCons(scip, row, SCIPconsGetHdlr(cons), cutname, lhs, rhs, islocal && (SCIPgetDepth(scip) > 0), FALSE, TRUE) );

      /* add coefficients from linear part */
      SCIP_CALL( SCIPaddVarsToRow(scip, *row, consdata->nlinvars, consdata->linvars, lincoefs) );

      /* add coefficients from quadratic part */
      assert(consdata->sepaquadvars != NULL || consdata->nquadvars == 0);
      SCIP_CALL( SCIPaddVarsToRow(scip, *row, consdata->nquadvars, consdata->sepaquadvars, coef) );

      SCIPdebugMessage("found cut <%s>, lhs=%g, rhs=%g, mincoef=%g, maxcoef=%g, range=%g, nnz=%d, violation=%g, efficacy=%g\n",
         SCIProwGetName(*row), lhs, rhs,
         mincoef, maxcoef, maxcoef/mincoef,
         SCIProwGetNNonz(*row), viol, rowefficacy);  /*lint !e414 */

      if( efficacy != NULL )
      {
         *efficacy = rowefficacy;

         /* check that our computed efficacy is > feastol, iff efficacy computed by row is > feastol
          * computing efficacy w.r.t. the LP solution makes only sense if the LP was solved to optimality (see bug 612)
          *
          * disabled these asserts as they can fail due to numerical reasons (cancelation when substracting big numbers),
          * as the order in which we add up the activity for the single terms can be different than the one that lp.c uses
          */
         /*
         assert(sol != NULL || SCIPgetLPSolstat(scip) == SCIP_LPSOLSTAT_OPTIMAL);
         assert((conshdlrdata->scaling != 'g') || (SCIPisFeasPositive(scip, rowefficacy) == SCIPisFeasPositive(scip, -SCIPgetRowSolFeasibility(scip, *row, sol)/MAX(1.0,SCIPgetRowMaxCoef(scip, *row)))));
         assert((conshdlrdata->scaling != 's') || (SCIPisFeasPositive(scip, rowefficacy) == SCIPisFeasPositive(scip, -SCIPgetRowSolFeasibility(scip, *row, sol)/MAX(1.0,MIN(REALABS(lhs),REALABS(rhs))))));
         assert((conshdlrdata->scaling != 'o') || (SCIPisFeasPositive(scip, rowefficacy) == SCIPisFeasPositive(scip, -SCIPgetRowSolFeasibility(scip, *row, sol))));
         */
      }
   }

   SCIPfreeBufferArray(scip, &coef);

   /* if coefficients for linear variables are different than those in constraint, then free array */
   if( lincoefs != consdata->lincoefs )
   {
      SCIPfreeBufferArray(scip, &lincoefs);
   }

   return SCIP_OKAY;
}

/** generates a cut based on linearization (if convex) or McCormick (if nonconvex) in a solution
 */
static
SCIP_RETCODE generateCutSol(
   SCIP*                 scip,               /**< SCIP data structure */
   SCIP_CONSHDLR*        conshdlr,           /**< constraint handler */
   SCIP_CONS*            cons,               /**< constraint */
   SCIP_SOL*             sol,                /**< solution where to generate cut, or NULL if LP solution should be used */
   SCIP_SOL*             refsol,             /**< reference point where to generate cut, or NULL if sol should be used */
   SCIP_SIDETYPE         violside,           /**< for which side a cut should be generated */
   SCIP_ROW**            row,                /**< storage for cut */
   SCIP_Real*            efficacy,           /**< buffer to store efficacy of row in reference solution, or NULL if not of interest */
   SCIP_Bool             checkcurvmultivar,  /**< are we allowed to check the curvature of a multivariate quadratic function, if not done yet */
   SCIP_Real             minefficacy         /**< minimal required efficacy (violation scaled by maximal absolute coefficient) */
   )
{
   SCIP_CONSDATA* consdata;
   SCIP_VAR*  var;
   SCIP_Real  lb;
   SCIP_Real  ub;
   SCIP_Real* ref;
   int j;

   assert(scip != NULL);
   assert(conshdlr != NULL);
   assert(cons != NULL);

   consdata = SCIPconsGetData(cons);
   assert(consdata != NULL);

   if( refsol == NULL )
      refsol = sol;

   /* get reference point */
   SCIP_CALL( SCIPallocBufferArray(scip, &ref, consdata->nquadvars) );
   for( j = 0; j < consdata->nquadvars; ++j )
   {
      var = consdata->quadvarterms[j].var;
      lb  = SCIPvarGetLbLocal(var);
      ub  = SCIPvarGetUbLocal(var);
      /* do not like variables at infinity */
      assert(!SCIPisInfinity(scip,  lb));
      assert(!SCIPisInfinity(scip, -ub));

      ref[j] = SCIPgetSolVal(scip, refsol, var);
      ref[j] = MIN(ub, MAX(lb, ref[j])); /* project value into bounds */
   }

   SCIP_CALL( generateCut(scip, conshdlr, cons, ref, sol, violside, row, efficacy, checkcurvmultivar, minefficacy) );

   SCIPfreeBufferArray(scip, &ref);

   return SCIP_OKAY;
}

/** tries to find a cut that intersects with an unbounded ray of the LP
 * for convex functions, we do this by linearizing in the feasible solution of the LPI
 * for nonconvex functions, we just call generateCutSol with the unbounded solution as reference point */
static
SCIP_RETCODE generateCutUnboundedLP(
   SCIP*                 scip,               /**< SCIP data structure */
   SCIP_CONSHDLR*        conshdlr,           /**< constraint handler */
   SCIP_CONS*            cons,               /**< constraint */
   SCIP_SIDETYPE         violside,           /**< for which side a cut should be generated */
   SCIP_ROW**            row,                /**< storage for cut */
   SCIP_Real*            rowrayprod,         /**< buffer to store product of ray with row coefficients, or NULL if not of interest */
   SCIP_Bool             checkcurvmultivar   /**< are we allowed to check the curvature of a multivariate quadratic function, if not done yet */
   )
{
   SCIP_CONSDATA* consdata;
   SCIP_BILINTERM* bilinterm;
   SCIP_VAR*  var;
   SCIP_Real* ref;
   SCIP_Real  matrixrayprod;
   SCIP_Real  linrayprod;
   SCIP_Real  quadrayprod;
   SCIP_Real  rayval;
   int i;
   int j;

   assert(scip != NULL);
   assert(conshdlr != NULL);
   assert(cons != NULL);
   assert(row  != NULL);
   assert(SCIPgetLPSolstat(scip) == SCIP_LPSOLSTAT_UNBOUNDEDRAY);

   consdata = SCIPconsGetData(cons);
   assert(consdata != NULL);

   *row = NULL;

   if( !SCIPhasPrimalRay(scip) )
   {
      SCIPdebugMessage("do not have primal ray, thus cannot resolve unboundedness\n");
      return SCIP_OKAY;
   }

   SCIP_CALL( checkCurvature(scip, cons, checkcurvmultivar) );
   if( (!consdata->isconvex && violside == SCIP_SIDETYPE_RIGHT) ||
      (!consdata->isconcave && violside == SCIP_SIDETYPE_LEFT) )
   {
      /* if not convex, just call generateCut and hope it's getting something useful */
      SCIP_CALL( generateCutSol(scip, conshdlr, cons, NULL, NULL, violside, row, NULL, FALSE, -SCIPinfinity(scip)) );

      /* compute product of cut coefficients with ray, if required */
      if( *row != NULL && rowrayprod != NULL )
      {
         *rowrayprod = 0.0;
         for( i = 0; i < SCIProwGetNNonz(*row); ++i )
         {
            assert(SCIProwGetCols(*row)[i] != NULL);
            var = SCIPcolGetVar(SCIProwGetCols(*row)[i]);
            assert(var != NULL);

            *rowrayprod += SCIProwGetVals(*row)[i] * SCIPgetPrimalRayVal(scip, var);
         }
      }

      return SCIP_OKAY;
   }

   /* we seek for a linearization of the quadratic function such that it intersects with the unbounded ray
    * that is, we need a reference point ref such that for the gradient g of xAx+bx in ref, we have
    *   <g, ray> > 0.0 if rhs is finite and <g, ray> < 0.0 if lhs is finite
    * Since g = 2*A*ref + b, we have <g, ray> = <2*A*ref + b, ray> = <ref, 2*A*ray> + <b,ray>
    * initially, for finite rhs, we set ref_i = 1.0 if (A*ray)_i > 0.0 and ref_i = -1.0 if (A*ray)_i < 0.0 (for finite lhs analog)
    * <ref, 2*A*ray> + <b,ray> is sufficiently larger 0.0, we call generateCut for this point, otherwise, we scale up ref
    */

   quadrayprod = 0.0; /* <ref, 2*A*ray> */
   linrayprod = 0.0;  /* <b, ray> */
   SCIP_CALL( SCIPallocBufferArray(scip, &ref, consdata->nquadvars) );
   for( i = 0; i < consdata->nquadvars; ++i )
   {
      var = consdata->quadvarterms[i].var;
      rayval = SCIPgetPrimalRayVal(scip, var);

      /* compute i-th entry of (2*A*ray) */
      matrixrayprod = 2.0 * consdata->quadvarterms[i].sqrcoef * rayval;
      for( j = 0; j < consdata->quadvarterms[i].nadjbilin; ++j )
      {
         bilinterm = &consdata->bilinterms[consdata->quadvarterms[i].adjbilin[j]];
         matrixrayprod += bilinterm->coef * SCIPgetPrimalRayVal(scip, bilinterm->var1 == var ? bilinterm->var2 : bilinterm->var1);
      }

      if( SCIPisPositive(scip, matrixrayprod) )
         ref[i] = (violside == SCIP_SIDETYPE_RIGHT ?  1.0 : -1.0);
      else if( SCIPisNegative(scip, matrixrayprod) )
         ref[i] = (violside == SCIP_SIDETYPE_RIGHT ? -1.0 :  1.0);
      else
         ref[i] = 0.0;

      quadrayprod += matrixrayprod * ref[i];
      linrayprod += consdata->quadvarterms[i].lincoef * rayval;
   }
   assert((violside == SCIP_SIDETYPE_RIGHT && quadrayprod >= 0.0) || (violside == SCIP_SIDETYPE_LEFT && quadrayprod <= 0.0));

   if( SCIPisZero(scip, quadrayprod) )
   {
      SCIPdebugMessage("ray is zero along cons <%s>\n", SCIPconsGetName(cons));
      SCIPfreeBufferArray(scip, &ref);
      return SCIP_OKAY;
   }

   /* add linear part to linrayprod */
   for( i = 0; i < consdata->nlinvars; ++i )
      linrayprod += consdata->lincoefs[i] * SCIPgetPrimalRayVal(scip, consdata->linvars[i]);

   SCIPdebugMessage("initially have <b,ray> = %g and <ref, 2*A*ref> = %g\n", linrayprod, quadrayprod);

   /* we scale the refpoint up, such that <ref, 2*A*ray> >= -2*<b, ray> (rhs finite) or <ref, 2*A*ray> <= -2*<b, ray> (lhs finite), if <b,ray> is not zero
    * if <b,ray> is zero, then we scale refpoint up if |<ref, 2*A*ray>| < 1.0
    */
   if( (!SCIPisZero(scip, linrayprod) && violside == SCIP_SIDETYPE_RIGHT && quadrayprod < -2*linrayprod) ||
      ( !SCIPisZero(scip, linrayprod) && violside == SCIP_SIDETYPE_LEFT  && quadrayprod > -2*linrayprod) ||
      (SCIPisZero(scip, linrayprod) && REALABS(quadrayprod) < 1.0) )
   {
      SCIP_Real scale;

      if( !SCIPisZero(scip, linrayprod) )
         scale = 2*REALABS(linrayprod/quadrayprod);  /*lint !e795 */
      else
         scale = 1.0/REALABS(quadrayprod);

      SCIPdebugMessage("scale refpoint by %g\n", scale);
      for( i = 0; i < consdata->nquadvars; ++i )
         ref[i] *= scale;
      quadrayprod *= scale;
   }

   if( rowrayprod != NULL )
      *rowrayprod = quadrayprod + linrayprod;

   SCIPdebugMessage("calling generateCut, expecting ray product %g\n", quadrayprod + linrayprod);
   SCIP_CALL( generateCut(scip, conshdlr, cons, ref, NULL, violside, row, NULL, FALSE, -SCIPinfinity(scip)) );

   SCIPfreeBufferArray(scip, &ref);

   return SCIP_OKAY;
}

/** tries to separate solution or LP solution by a linear cut
 * 
 *  assumes that constraint violations have been computed 
 */
static
SCIP_RETCODE separatePoint(
   SCIP*                 scip,               /**< SCIP data structure */
   SCIP_CONSHDLR*        conshdlr,           /**< quadratic constraints handler */
   SCIP_CONS**           conss,              /**< constraints */
   int                   nconss,             /**< number of constraints */
   int                   nusefulconss,       /**< number of constraints that seem to be useful */
   SCIP_SOL*             sol,                /**< solution to separate, or NULL if LP solution should be used */
   SCIP_Real             minefficacy,        /**< minimal efficacy of a cut if it should be added to the LP */
   SCIP_Bool             inenforcement,      /**< whether we are in constraint enforcement */
   SCIP_RESULT*          result,             /**< result of separation */
   SCIP_Real*            bestefficacy        /**< buffer to store best efficacy of a cut that was added to the LP, if found; or NULL if not of interest */
   )
{
   SCIP_CONSHDLRDATA* conshdlrdata;
   SCIP_CONSDATA*     consdata;
   SCIP_Real          efficacy;
   SCIP_Real          actminefficacy;
   SCIP_SIDETYPE      violside;
   int                c;
   SCIP_ROW*          row;

   assert(scip != NULL);
   assert(conshdlr != NULL);
   assert(conss != NULL || nconss == 0);
   assert(nusefulconss <= nconss);
   assert(result != NULL);

   *result = SCIP_FEASIBLE;

   conshdlrdata = SCIPconshdlrGetData(conshdlr);
   assert(conshdlrdata != NULL);

   if( bestefficacy != NULL )
      *bestefficacy = 0.0;

   for( c = 0; c < nconss; ++c )
   {
      assert(conss != NULL);
      consdata = SCIPconsGetData(conss[c]);
      assert(consdata != NULL);

      if( SCIPisGT(scip, consdata->lhsviol, SCIPfeastol(scip)) || SCIPisGT(scip, consdata->rhsviol, SCIPfeastol(scip)) )
      {
         /* we are not feasible anymore */
         if( *result == SCIP_FEASIBLE )
            *result = SCIP_DIDNOTFIND;

         violside = SCIPisGT(scip, consdata->lhsviol, SCIPfeastol(scip)) ? SCIP_SIDETYPE_LEFT : SCIP_SIDETYPE_RIGHT;

         /* actual minimal efficacy */
         actminefficacy = inenforcement && ((violside == SCIP_SIDETYPE_RIGHT && consdata->isconvex ) || (violside == SCIP_SIDETYPE_LEFT && consdata->isconcave))
            ? (SCIPgetRelaxFeastolFactor(scip) > 0.0 ? SCIPepsilon(scip) : SCIPfeastol(scip))
            : minefficacy;

         /* generate cut */
         if( sol == NULL && SCIPgetLPSolstat(scip) == SCIP_LPSOLSTAT_UNBOUNDEDRAY )
         {
            /* if the LP is unbounded, then we need a cut that cuts into the direction of a hopefully existing primal ray
             * that is, assume a ray r is given such that p + t*r is feasible for the LP for all t >= t_0 and some p
             * given a cut lhs <= <c,x> <= rhs, we check whether it imposes an upper bound on t and thus bounds the ray
             * this is given if rhs < infinity and <c,r> > 0, since we then enforce <c,p+t*r> = <c,p> + t<c,r> <= rhs, i.e., t <= (rhs - <c,p>)/<c,r>
             * similar, lhs > -infinity and <c,r> < 0 is good
             */
            SCIP_Real rayprod;
            SCIP_Real norm;

            rayprod = 0.0; /* for compiler */
            SCIP_CALL( generateCutUnboundedLP(scip, conshdlr, conss[c], violside, &row, &rayprod, conshdlrdata->checkcurvature) );

            if( row != NULL )
            {
               if( !SCIPisInfinity(scip, SCIProwGetRhs(row)) && SCIPisPositive(scip, rayprod) )
                  efficacy =  rayprod;
               else if( !SCIPisInfinity(scip, -SCIProwGetLhs(row)) && SCIPisNegative(scip, rayprod) )
                  efficacy = -rayprod;
               else
                  efficacy = 0.0;

               switch( conshdlrdata->scaling )
               {
               case 'o' :
                  break;

               case 'g' :
                  /* in difference to SCIPgetCutEfficacy, we scale by norm only if the norm is > 1.0 this avoid finding
                   * cuts efficient which are only very slightly violated CPLEX does not seem to scale row
                   * coefficients up too also we use infinity norm, since that seem to be the usual scaling strategy
                   * in LP solvers (equilibrium scaling) */
                  norm = SCIPgetRowMaxCoef(scip, row);
                  efficacy /= MAX(1.0, norm);
                  break;

               case 's' :
               {
                  SCIP_Real abslhs = REALABS(SCIProwGetLhs(row));
                  SCIP_Real absrhs = REALABS(SCIProwGetRhs(row));
                  SCIP_Real minval = MIN(abslhs, absrhs);

                  efficacy /= MAX(1.0, minval);
                  break;
               }

               default:
                  SCIPerrorMessage("Unknown scaling method '%c'.", conshdlrdata->scaling);
                  SCIPABORT();
                  return SCIP_INVALIDDATA;  /*lint !e527*/
               }
            }
         }
         else
         {
            /* @todo If convex, can we easily move the refpoint closer to the feasible region to get a stronger cut?
             * E.g., use bisection on the line between LP solution and best primal (or LP interior)
             */
            SCIP_CALL( generateCutSol(scip, conshdlr, conss[c], sol, NULL, violside, &row, &efficacy, conshdlrdata->checkcurvature, actminefficacy) );
            /* @todo If generation failed not because of low efficacy, then probably because of numerical issues;
             * if the constraint is convex and we are desperate to get a cut, then we may try again with a better chosen reference point
             */
         }

         if( row == NULL ) /* failed to generate cut */
            continue;

         if( SCIPisGT(scip, efficacy, actminefficacy) && SCIPisCutApplicable(scip, row) )  /*lint !e644 */
         {
            SCIP_Bool infeasible;

            /* cut cuts off solution */
            SCIP_CALL( SCIPaddCut(scip, sol, row, FALSE /* forcecut */, &infeasible) );
            if( infeasible )
            {
               SCIPdebugMessage("cut for constraint <%s> is infeasible -> cutoff.\n", SCIPconsGetName(conss[c]));
               *result = SCIP_CUTOFF;
            }
            else
            {
               SCIPdebugMessage("add cut with efficacy %g for constraint <%s> violated by %g\n", efficacy,
                  SCIPconsGetName(conss[c]), consdata->lhsviol+consdata->rhsviol);
               *result = SCIP_SEPARATED;
            }
            SCIP_CALL( SCIPresetConsAge(scip, conss[c]) );

            /* mark row as not removable from LP for current node, if in enforcement */
            if( inenforcement && !conshdlrdata->enfocutsremovable )
               SCIPmarkRowNotRemovableLocal(scip, row);
         }
         if( bestefficacy != NULL && efficacy > *bestefficacy )
            *bestefficacy = efficacy;

         SCIP_CALL( SCIPreleaseRow (scip, &row) );
      }

      if( *result == SCIP_CUTOFF )
         break;

      /* enforce only useful constraints
       * others are only checked and enforced if we are still feasible or have not found a separating cut yet
       */
      if( c >= nusefulconss && *result == SCIP_SEPARATED )
         break;
   }

   return SCIP_OKAY;
}

/** adds linearizations cuts for convex constraints w.r.t. a given reference point to cutpool and sepastore
 * if separatedlpsol is not NULL, then a cut that separates the LP solution is added to the sepastore and is forced to enter the LP
 * if separatedlpsol is not NULL, but cut does not separate the LP solution, then it is added to the cutpool only
 * if separatedlpsol is NULL, then cut is added to cutpool only
 */
static
SCIP_RETCODE addLinearizationCuts(
   SCIP*                 scip,               /**< SCIP data structure */
   SCIP_CONSHDLR*        conshdlr,           /**< quadratic constraints handler */
   SCIP_CONS**           conss,              /**< constraints */
   int                   nconss,             /**< number of constraints */
   SCIP_SOL*             ref,                /**< reference point where to linearize, or NULL for LP solution */
   SCIP_Bool*            separatedlpsol,     /**< buffer to store whether a cut that separates the current LP solution was found and added to LP, or NULL if adding to cutpool only */
   SCIP_Real             minefficacy         /**< minimal efficacy of a cut when checking for separation of LP solution */
   )
{
   SCIP_CONSHDLRDATA* conshdlrdata;
   SCIP_CONSDATA* consdata;
   SCIP_Bool addedtolp;
   SCIP_ROW* row;
   int c;

   assert(scip != NULL);
   assert(conshdlr != NULL);
   assert(conss != NULL || nconss == 0);

   conshdlrdata = SCIPconshdlrGetData(conshdlr);
   assert(conshdlrdata != NULL);

   if( separatedlpsol != NULL )
      *separatedlpsol = FALSE;

   for( c = 0; c < nconss; ++c )
   {
      assert(conss[c] != NULL);  /*lint !e613 */

      if( SCIPconsIsLocal(conss[c]) )  /*lint !e613 */
         continue;

      SCIP_CALL( checkCurvature(scip, conss[c], conshdlrdata->checkcurvature) );  /*lint !e613 */

      consdata = SCIPconsGetData(conss[c]);  /*lint !e613 */
      assert(consdata != NULL);

      if( consdata->isconvex && !SCIPisInfinity(scip, consdata->rhs) )
      {
         SCIP_CALL( generateCutSol(scip, conshdlr, conss[c], NULL, ref, SCIP_SIDETYPE_RIGHT, &row, NULL, conshdlrdata->checkcurvature, -SCIPinfinity(scip)) );  /*lint !e613 */
      }
      else if( consdata->isconcave && !SCIPisInfinity(scip, -consdata->lhs) )
      {
         SCIP_CALL( generateCutSol(scip, conshdlr, conss[c], NULL, ref, SCIP_SIDETYPE_LEFT,  &row, NULL, conshdlrdata->checkcurvature, -SCIPinfinity(scip)) );  /*lint !e613 */
      }
      else
         continue;

      if( row == NULL )
         continue;

      addedtolp = FALSE;

      /* if caller wants, then check if cut separates LP solution and add to sepastore if so */
      if( separatedlpsol != NULL )
      {
         SCIP_Real efficacy;
         SCIP_Real norm;

         efficacy = -SCIPgetRowLPFeasibility(scip, row);
         switch( conshdlrdata->scaling )
         {
         case 'o' :
            break;

         case 'g' :
            /* in difference to SCIPgetCutEfficacy, we scale by norm only if the norm is > 1.0 this avoid finding cuts
             * efficient which are only very slightly violated CPLEX does not seem to scale row coefficients up too
             * also we use infinity norm, since that seem to be the usual scaling strategy in LP solvers (equilibrium
             * scaling) */
            norm = SCIPgetRowMaxCoef(scip, row);
            efficacy /= MAX(1.0, norm);
            break;

         case 's' :
         {
            SCIP_Real abslhs = REALABS(SCIProwGetLhs(row));
            SCIP_Real absrhs = REALABS(SCIProwGetRhs(row));
            SCIP_Real minval = MIN(abslhs, absrhs);

            efficacy /= MAX(1.0, minval);
            break;
         }

         default:
            SCIPerrorMessage("Unknown scaling method '%c'.", conshdlrdata->scaling);
            SCIPABORT();
            return SCIP_INVALIDDATA;  /*lint !e527*/
         }

         if( efficacy >= minefficacy )
         {
            SCIP_Bool infeasible;

            *separatedlpsol = TRUE;
            addedtolp = TRUE;
            SCIP_CALL( SCIPaddCut(scip, NULL, row, TRUE, &infeasible) );
            assert( ! infeasible );
            SCIPdebugMessage("added linearization cut <%s> to LP, efficacy = %g\n", SCIProwGetName(row), efficacy);
         }
      }

      if( !SCIProwIsLocal(row) && !addedtolp )
      {
         SCIP_CALL( SCIPaddPoolCut(scip, row) );
         SCIPdebugMessage("added linearization cut <%s> to cutpool\n", SCIProwGetName(row));
      }

      SCIP_CALL( SCIPreleaseRow(scip, &row) );
   }

   return SCIP_OKAY;
}

/** processes the event that a new primal solution has been found */
static
SCIP_DECL_EVENTEXEC(processNewSolutionEvent)
{
   SCIP_CONSHDLRDATA* conshdlrdata;
   SCIP_CONSHDLR* conshdlr;
   SCIP_CONS**    conss;
   int            nconss;
   SCIP_SOL*      sol;

   assert(scip != NULL);
   assert(event != NULL);
   assert(eventdata != NULL);
   assert(eventhdlr != NULL);

   assert((SCIPeventGetType(event) & SCIP_EVENTTYPE_SOLFOUND) != 0);

   conshdlr = (SCIP_CONSHDLR*)eventdata;

   nconss = SCIPconshdlrGetNConss(conshdlr);

   if( nconss == 0 )
      return SCIP_OKAY;

   sol = SCIPeventGetSol(event);
   assert(sol != NULL);

   conshdlrdata = SCIPconshdlrGetData(conshdlr);
   assert(conshdlrdata != NULL);

   /* we are only interested in solution coming from some heuristic other than trysol, but not from the tree
    * the reason for ignoring trysol solutions is that they may come from an NLP solve in sepalp, where we already added linearizations,
    * or are from the tree, but postprocessed via proposeFeasibleSolution
    */
   if( SCIPsolGetHeur(sol) == NULL || SCIPsolGetHeur(sol) == conshdlrdata->trysolheur )
      return SCIP_OKAY;

   conss = SCIPconshdlrGetConss(conshdlr);
   assert(conss != NULL);

   SCIPdebugMessage("caught new sol event %x from heur <%s>; have %d conss\n", SCIPeventGetType(event), SCIPheurGetName(SCIPsolGetHeur(sol)), nconss);

   SCIP_CALL( addLinearizationCuts(scip, conshdlr, conss, nconss, sol, NULL, 0.0) );

   return SCIP_OKAY;
}

/** computes the infeasibilities of variables from the convexification gaps in the constraints and notifies the branching rule about them
 */
static
SCIP_RETCODE registerVariableInfeasibilities(
   SCIP*                 scip,               /**< SCIP data structure */
   SCIP_CONSHDLR*        conshdlr,           /**< constraint handler */
   SCIP_CONS**           conss,              /**< constraints to check */
   int                   nconss,             /**< number of constraints to check */
   int*                  nnotify             /**< counter for number of notifications performed */
   )
{
   SCIP_CONSDATA*     consdata;
   int                c;
   int                j;
   SCIP_Bool          xbinary;
   SCIP_Bool          ybinary;
   SCIP_Bool          xunbounded;
   SCIP_Bool          yunbounded;
   SCIP_VAR*          x;
   SCIP_VAR*          y;
   SCIP_Real          xlb;
   SCIP_Real          xub;
   SCIP_Real          xval;
   SCIP_Real          ylb;
   SCIP_Real          yub;
   SCIP_Real          yval;
   SCIP_Real          gap;
   SCIP_Real          coef_;

   assert(scip != NULL);
   assert(conshdlr != NULL);
   assert(conss != NULL || nconss == 0);

   *nnotify = 0;
   yval = SCIP_INVALID;
   xval = SCIP_INVALID;

   for( c = 0; c < nconss; ++c )
   {
      assert(conss != NULL);
      consdata = SCIPconsGetData(conss[c]);
      assert(consdata != NULL);

      if( !consdata->nquadvars )
         continue;

      if( (!SCIPisGT(scip, consdata->lhsviol, SCIPfeastol(scip)) || consdata->isconcave) &&
         ( !SCIPisGT(scip, consdata->rhsviol, SCIPfeastol(scip)) || consdata->isconvex ) )
         continue;
      SCIPdebugMessage("cons %s violation: %g %g  convex: %u %u\n", SCIPconsGetName(conss[c]), consdata->lhsviol, consdata->rhsviol, consdata->isconvex, consdata->isconcave);

      /* square terms */
      for( j = 0; j < consdata->nquadvars; ++j )
      {
         x = consdata->quadvarterms[j].var;
         if( (SCIPisGT(scip, consdata->rhsviol, SCIPfeastol(scip)) && consdata->quadvarterms[j].sqrcoef < 0) ||
            ( SCIPisGT(scip, consdata->lhsviol, SCIPfeastol(scip)) && consdata->quadvarterms[j].sqrcoef > 0) )
         {
            xlb = SCIPvarGetLbLocal(x);
            xub = SCIPvarGetUbLocal(x);
            if( SCIPisRelEQ(scip, xlb, xub) )
            {
               SCIPdebugMessage("ignore fixed variable <%s>[%g, %g], diff %g\n", SCIPvarGetName(x), xlb, xub, xub-xlb);
               continue;
            }

            xval = SCIPgetSolVal(scip, NULL, x);

            /* if variable is at bounds, then no need to branch, since secant is exact there */
            if( SCIPisLE(scip, xval, xlb) || SCIPisGE(scip, xval, xub) )
               continue;

            if( SCIPisInfinity(scip, -xlb) || SCIPisInfinity(scip, xub) )
               gap = SCIPinfinity(scip);
            else
               gap = (xval-xlb)*(xub-xval)/(1+2*ABS(xval));
            assert(!SCIPisFeasNegative(scip, gap));
            SCIP_CALL( SCIPaddExternBranchCand(scip, x, MAX(gap, 0.0), SCIP_INVALID) );
            ++*nnotify;
         }
      }

      /* bilinear terms */
      for( j = 0; j < consdata->nbilinterms; ++j )
      {
         /* if any of the variables if fixed, then it actually behaves like a linear term, so we don't need to branch on it */
         x = consdata->bilinterms[j].var1;
         xlb = SCIPvarGetLbLocal(x);
         xub = SCIPvarGetUbLocal(x);
         if( SCIPisRelEQ(scip, xlb, xub) )
            continue;

         y = consdata->bilinterms[j].var2;
         ylb = SCIPvarGetLbLocal(y);
         yub = SCIPvarGetUbLocal(y);
         if( SCIPisRelEQ(scip, ylb, yub) )
            continue;

         xunbounded = SCIPisInfinity(scip, -xlb) || SCIPisInfinity(scip, xub);
         yunbounded = SCIPisInfinity(scip, -ylb) || SCIPisInfinity(scip, yub);

         /* compute gap, if both variable are bounded */
         gap = SCIPinfinity(scip);
         if( !xunbounded && !yunbounded )
         {
            xval = SCIPgetSolVal(scip, NULL, x);
            yval = SCIPgetSolVal(scip, NULL, y);

            /* if both variables are at one of its bounds, then no need to branch, since McCormick is exact there */
            if( (SCIPisLE(scip, xval, xlb) || SCIPisGE(scip, xval, xub)) &&
               ( SCIPisLE(scip, yval, ylb) || SCIPisGE(scip, yval, yub)) )
               continue;

            xval = MAX(xlb, MIN(xval, xub));
            yval = MAX(ylb, MIN(yval, yub));

            coef_ = SCIPisGT(scip, consdata->lhsviol, SCIPfeastol(scip)) ? -consdata->bilinterms[j].coef : consdata->bilinterms[j].coef;
            if( coef_ > 0.0 )
            {
               if( (xub-xlb)*yval + (yub-ylb)*xval <= xub*yub - xlb*ylb )
                  gap = (xval*yval - xlb*yval - ylb*xval + xlb*ylb) / (1+sqrt(xval*xval + yval*yval));
               else
                  gap = (xval*yval - xval*yub - yval*xub + xub*yub) / (1+sqrt(xval*xval + yval*yval));
            }
            else
            { /* coef_ < 0 */
               if( (xub-xlb)*yval - (yub-ylb)*xval <= xub*ylb - xlb*yub )
                  gap = -(xval*yval - xval*ylb - yval*xub + xub*ylb) / (1+sqrt(xval*xval + yval*yval));
               else
                  gap = -(xval*yval - xval*yub - yval*xlb + xlb*yub) / (1+sqrt(xval*xval + yval*yval));
            }

            assert(!SCIPisNegative(scip, gap / MAX3(MAX(REALABS(xlb), REALABS(xub)), MAX(REALABS(ylb), REALABS(yub)), 1.0)));  /*lint !e666*/
            if( gap < 0.0 )
               gap = 0.0;
         }

         /* if one of the variables is binary or integral with domain width 1, then branching on this makes the term linear, so prefer this */
         xbinary = SCIPvarIsBinary(x) || (SCIPvarIsIntegral(x) && xub - xlb < 1.5);
         ybinary = SCIPvarIsBinary(y) || (SCIPvarIsIntegral(y) && yub - ylb < 1.5);
         if( xbinary )
         {
            SCIP_CALL( SCIPaddExternBranchCand(scip, x, gap, SCIP_INVALID) );
            ++*nnotify;
         }
         if( ybinary )
         {
            SCIP_CALL( SCIPaddExternBranchCand(scip, y, gap, SCIP_INVALID) );
            ++*nnotify;
         }
         if( xbinary || ybinary )
            continue;

         /* if one of the variables is unbounded, then branch on it first */
         if( xunbounded )
         {
            SCIP_CALL( SCIPaddExternBranchCand(scip, x, gap, SCIP_INVALID) );
            ++*nnotify;
         }
         if( yunbounded )
         {
            SCIP_CALL( SCIPaddExternBranchCand(scip, y, gap, SCIP_INVALID) );
            ++*nnotify;
         }
         if( xunbounded || yunbounded )
            continue;

         /* if both variables are integral, prefer the one with the smaller domain, so variable gets fixed soon
          * does not seem to work well on tln instances, so disable for now and may look at it later again
          */
#ifdef BRANCHTOLINEARITY
         if( SCIPvarIsIntegral(x) && SCIPvarIsIntegral(y) )
         {
            if( SCIPisLT(scip, xub-xlb, yub-ylb) )
            {
               SCIP_CALL( SCIPaddExternBranchCand(scip, x, gap, SCIP_INVALID) );
               ++*nnotify;
               continue;
            }
            if( SCIPisGT(scip, xub-xlb, yub-ylb) )
            {
               SCIP_CALL( SCIPaddExternBranchCand(scip, y, gap, SCIP_INVALID) );
               ++*nnotify;
               continue;
            }
         }
#endif

         /* in the regular case, suggest those variables which are not at its bounds for branching
          * this is, because after branching both variables will be one the bounds, and McCormick will be exact then */
         if( !SCIPisLE(scip, xval, xlb) && !SCIPisGE(scip, xval, xub) )
         {
            SCIP_CALL( SCIPaddExternBranchCand(scip, x, gap, SCIP_INVALID) );
            ++*nnotify;
         }
         if( !SCIPisLE(scip, yval, ylb) && !SCIPisGE(scip, yval, yub) )
         {
            SCIP_CALL( SCIPaddExternBranchCand(scip, y, gap, SCIP_INVALID) );
            ++*nnotify;
         }
      }
   }

   SCIPdebugMessage("registered %d branching candidates\n", *nnotify);

   return SCIP_OKAY;
}

/** registers a quadratic variable from a violated constraint as branching candidate that has a large absolute value in the LP relaxation */
static
SCIP_RETCODE registerLargeLPValueVariableForBranching(
   SCIP*                 scip,               /**< SCIP data structure */
   SCIP_CONS**           conss,              /**< constraints */
   int                   nconss,             /**< number of constraints */
   SCIP_VAR**            brvar               /**< buffer to store branching variable */
   )
{
   SCIP_CONSDATA*      consdata;
   SCIP_Real           val;
   SCIP_Real           brvarval;
   int                 i;
   int                 c;

   assert(scip  != NULL);
   assert(conss != NULL || nconss == 0);

   *brvar = NULL;
   brvarval = -1.0;

   for( c = 0; c < nconss; ++c )
   {
      assert(conss != NULL);
      consdata = SCIPconsGetData(conss[c]);
      assert(consdata != NULL);

      if( !SCIPisGT(scip, consdata->lhsviol, SCIPfeastol(scip)) && !SCIPisGT(scip, consdata->rhsviol, SCIPfeastol(scip)) )
         continue;

      for( i = 0; i < consdata->nquadvars; ++i )
      {
         /* do not propose fixed variables */
         if( SCIPisRelEQ(scip, SCIPvarGetLbLocal(consdata->quadvarterms[i].var), SCIPvarGetUbLocal(consdata->quadvarterms[i].var)) )
            continue;
         val = SCIPgetSolVal(scip, NULL, consdata->quadvarterms[i].var);
         if( ABS(val) > brvarval )
         {
            brvarval = ABS(val);
            *brvar = consdata->quadvarterms[i].var;
         }
      }
   }

   if( *brvar != NULL )
   {
      SCIP_CALL( SCIPaddExternBranchCand(scip, *brvar, brvarval, SCIP_INVALID) );
   }

   return SCIP_OKAY;
}

/** replaces violated quadratic constraints where all quadratic variables are fixed by linear constraints */
static
SCIP_RETCODE replaceByLinearConstraints(
   SCIP*                 scip,               /**< SCIP data structure */
   SCIP_CONS**           conss,              /**< constraints */
   int                   nconss,             /**< number of constraints */
   SCIP_Bool*            addedcons,          /**< buffer to store whether a linear constraint was added */
   SCIP_Bool*            reduceddom,         /**< whether a domain has been reduced */
   SCIP_Bool*            infeasible          /**< whether we detected infeasibility */
   )
{
   SCIP_CONS*          cons;
   SCIP_CONSDATA*      consdata;
   SCIP_RESULT         checkresult;
   SCIP_Real           constant;
   SCIP_Real           val1;
   SCIP_Real           val2;
   int                 i;
   int                 c;

   assert(scip  != NULL);
   assert(conss != NULL || nconss == 0);
   assert(addedcons != NULL);
   assert(reduceddom != NULL);
   assert(infeasible != NULL);

   *addedcons = FALSE;
   *reduceddom = FALSE;
   *infeasible = FALSE;

   for( c = 0; c < nconss; ++c )
   {
      assert(conss != NULL);
      consdata = SCIPconsGetData(conss[c]);
      assert(consdata != NULL);

      if( !SCIPisGT(scip, consdata->lhsviol, SCIPfeastol(scip)) && !SCIPisGT(scip, consdata->rhsviol, SCIPfeastol(scip)) )
         continue;

      constant = 0.0;

      for( i = 0; i < consdata->nquadvars; ++i )
      {
         /* variables should be fixed if constraint is violated */
         assert(SCIPisRelEQ(scip, SCIPvarGetLbLocal(consdata->quadvarterms[i].var), SCIPvarGetUbLocal(consdata->quadvarterms[i].var)));

         val1 = (SCIPvarGetUbLocal(consdata->quadvarterms[i].var) + SCIPvarGetLbLocal(consdata->quadvarterms[i].var)) / 2.0;
         constant += (consdata->quadvarterms[i].lincoef + consdata->quadvarterms[i].sqrcoef * val1) * val1;
      }

      for( i = 0; i < consdata->nbilinterms; ++i )
      {
         val1 = (SCIPvarGetUbLocal(consdata->bilinterms[i].var1) + SCIPvarGetLbLocal(consdata->bilinterms[i].var1)) / 2.0;
         val2 = (SCIPvarGetUbLocal(consdata->bilinterms[i].var2) + SCIPvarGetLbLocal(consdata->bilinterms[i].var2)) / 2.0;
         constant += consdata->bilinterms[i].coef * val1 * val2;
      }

      /* check if we have a bound change */
      if ( consdata->nlinvars == 1 )
      {
         SCIP_Bool tightened;
         SCIP_Real coef;
         SCIP_Real lhs;
         SCIP_Real rhs;

         coef = *consdata->lincoefs;

         /* compute lhs/rhs */
         if ( SCIPisInfinity(scip, -consdata->lhs) )
            lhs = -SCIPinfinity(scip);
         else
            lhs = consdata->lhs - constant;

         if ( SCIPisInfinity(scip, consdata->rhs) )
            rhs = SCIPinfinity(scip);
         else
            rhs = consdata->rhs - constant;

         SCIPdebugMessage("Linear constraint with one variable: %g <= %g <%s> <= %g\n", lhs, coef, SCIPvarGetName(*consdata->linvars), rhs);

         /* possibly correct lhs/rhs */
         assert( ! SCIPisZero(scip, coef) );
         if ( coef >= 0.0 )
         {
            if ( ! SCIPisInfinity(scip, -lhs) )
               lhs /= coef;
            if ( ! SCIPisInfinity(scip, rhs) )
               rhs /= coef;
         }
         else
         {
            SCIP_Real h;
            h = rhs;
            if ( ! SCIPisInfinity(scip, -lhs) )
               rhs = lhs/coef;
            else
               rhs = SCIPinfinity(scip);

            if ( ! SCIPisInfinity(scip, h) )
               lhs = h/coef;
            else
               lhs = -SCIPinfinity(scip);
         }
         SCIPdebugMessage("Linear constraint is a bound: %g <= <%s> <= %g\n", lhs, SCIPvarGetName(*consdata->linvars), rhs);

         if ( ! SCIPisInfinity(scip, -lhs) )
         {
            SCIP_CALL( SCIPtightenVarLb(scip, *consdata->linvars, lhs, TRUE, infeasible, &tightened) );
            if ( *infeasible )
            {
               SCIPdebugMessage("Lower bound leads to infeasibility.\n");
               return SCIP_OKAY;
            }
            if ( tightened )
            {
               SCIPdebugMessage("Lower boundx changed.\n");
               *reduceddom = TRUE;
               return SCIP_OKAY;
            }
         }

         if ( ! SCIPisInfinity(scip, rhs) )
         {
            SCIP_CALL( SCIPtightenVarUb(scip, *consdata->linvars, rhs, TRUE, infeasible, &tightened) );
            if ( *infeasible )
            {
               SCIPdebugMessage("Upper bound leads to infeasibility.\n");
               return SCIP_OKAY;
            }
            if ( tightened )
            {
               SCIPdebugMessage("Upper bound changed.\n");
               *reduceddom = TRUE;
               return SCIP_OKAY;
            }
         }
      }
      else
      {
         SCIP_CALL( SCIPcreateConsLinear(scip, &cons, SCIPconsGetName(conss[c]),
               consdata->nlinvars, consdata->linvars, consdata->lincoefs,
               (SCIPisInfinity(scip, -consdata->lhs) ? -SCIPinfinity(scip) : (consdata->lhs - constant)),
               (SCIPisInfinity(scip,  consdata->rhs) ?  SCIPinfinity(scip) : (consdata->rhs - constant)),
               SCIPconsIsInitial(conss[c]), SCIPconsIsSeparated(conss[c]), SCIPconsIsEnforced(conss[c]),
               SCIPconsIsChecked(conss[c]), SCIPconsIsPropagated(conss[c]),  TRUE,
               SCIPconsIsModifiable(conss[c]), SCIPconsIsDynamic(conss[c]), SCIPconsIsRemovable(conss[c]),
               SCIPconsIsStickingAtNode(conss[c])) );

         SCIPdebugMessage("replace quadratic constraint <%s> by linear constraint after all quadratic vars have been fixed\n", SCIPconsGetName(conss[c]) );
         SCIPdebugPrintCons(scip, cons, NULL);

         SCIP_CALL( SCIPcheckCons(scip, cons, NULL, FALSE, FALSE, FALSE, &checkresult) );

         if( checkresult != SCIP_INFEASIBLE && SCIPgetLPSolstat(scip) == SCIP_LPSOLSTAT_OPTIMAL )
         {
            SCIPdebugMessage("linear constraint is feasible and LP optimal, thus do not add\n");
         }
         else
         {
            SCIP_CALL( SCIPaddConsLocal(scip, cons, NULL) );
            *addedcons = TRUE;
         }
         SCIP_CALL( SCIPreleaseCons(scip, &cons) );
      }
      SCIP_CALL( SCIPdelConsLocal(scip, conss[c]) );
   }

   return SCIP_OKAY;
}

/* tightens a lower bound on a variable and checks the result */
static
SCIP_RETCODE propagateBoundsTightenVarLb(
   SCIP*                 scip,               /**< SCIP data structure */ 
   SCIP_CONS*            cons,               /**< constraint where we currently propagate */
   SCIP_Real             intervalinfty,      /**< infinity value used in interval operations */
   SCIP_VAR*             var,                /**< variable which domain we might reduce */
   SCIP_Real             bnd,                /**< new lower bound for variable */
   SCIP_RESULT*          result,             /**< result to update if there was a tightening or cutoff */
   int*                  nchgbds             /**< counter to increase if a bound was tightened */
   )
{
   SCIP_Bool infeas;
   SCIP_Bool tightened;

   assert(scip != NULL);
   assert(cons != NULL);
   assert(intervalinfty > 0.0);
   assert(bnd > -intervalinfty);
   assert(var != NULL);
   assert(result != NULL);
   assert(*result == SCIP_DIDNOTFIND || *result == SCIP_REDUCEDDOM);
   assert(nchgbds != NULL);

   /* new bound is no improvement */
   if( SCIPisHugeValue(scip, -bnd) || SCIPisLE(scip, bnd, SCIPvarGetLbLocal(var)) )
      return SCIP_OKAY;

   if( SCIPisInfinity(scip, bnd) )
   { /* domain will be outside [-infty, +infty] -> declare node infeasible */
      *result = SCIP_CUTOFF;
      SCIP_CALL( SCIPresetConsAge(scip, cons) );
      return SCIP_OKAY;
   }

   /* new lower bound is very low (between -intervalinfty and -SCIPinfinity()) */
   if( SCIPisInfinity(scip, -bnd) )
      return SCIP_OKAY;

   bnd = SCIPadjustedVarLb(scip, var, bnd);
   SCIP_CALL( SCIPtightenVarLb(scip, var, bnd, FALSE, &infeas, &tightened) );
   if( infeas )
   {
      SCIPdebugMessage("%s found constraint <%s> infeasible due to tightened lower bound %g for variable <%s>\n", SCIPinProbing(scip) ? "in probing" : "", SCIPconsGetName(cons), bnd, SCIPvarGetName(var));
      *result = SCIP_CUTOFF;
      SCIP_CALL( SCIPresetConsAge(scip, cons) );
      return SCIP_OKAY;
   }
   if( tightened )
   {
      SCIPdebugMessage("%s tightened lower bound of variable <%s> in constraint <%s> to %g\n", SCIPinProbing(scip) ? "in probing" : "", SCIPvarGetName(var), SCIPconsGetName(cons), bnd);
      ++*nchgbds;
      *result = SCIP_REDUCEDDOM;
      SCIP_CALL( SCIPresetConsAge(scip, cons) );
   }

   return SCIP_OKAY;
}

/* tightens an upper bound on a variable and checks the result */
static
SCIP_RETCODE propagateBoundsTightenVarUb(
   SCIP*                 scip,               /**< SCIP data structure */ 
   SCIP_CONS*            cons,               /**< constraint where we currently propagate */
   SCIP_Real             intervalinfty,      /**< infinity value used in interval operations */
   SCIP_VAR*             var,                /**< variable which domain we might reduce */
   SCIP_Real             bnd,                /**< new upper bound for variable */
   SCIP_RESULT*          result,             /**< result to update if there was a tightening or cutoff */
   int*                  nchgbds             /**< counter to increase if a bound was tightened */
   )
{
   SCIP_Bool infeas;
   SCIP_Bool tightened;

   assert(scip != NULL);
   assert(cons != NULL);
   assert(intervalinfty > 0.0);
   assert(bnd < intervalinfty);
   assert(var != NULL);
   assert(result != NULL);
   assert(*result == SCIP_DIDNOTFIND || *result == SCIP_REDUCEDDOM);
   assert(nchgbds != NULL);

   /* new bound is no improvement */
   if( SCIPisHugeValue(scip, bnd) || SCIPisGE(scip, bnd, SCIPvarGetUbLocal(var)) )
      return SCIP_OKAY;

   if( SCIPisInfinity(scip, -bnd) )
   { /* domain will be outside [-infty, +infty] -> declare node infeasible */
      *result = SCIP_CUTOFF;
      SCIP_CALL( SCIPresetConsAge(scip, cons) );
      return SCIP_OKAY;
   }

   /* new upper bound is very high (between SCIPinfinity() and intervalinfty) */
   if( SCIPisInfinity(scip, bnd) )
      return SCIP_OKAY;

   bnd = SCIPadjustedVarUb(scip, var, bnd);
   SCIP_CALL( SCIPtightenVarUb(scip, var, bnd, FALSE, &infeas, &tightened) );
   if( infeas )
   {
      SCIPdebugMessage("%s found constraint <%s> infeasible due to tightened upper bound %g for variable <%s>\n", SCIPinProbing(scip) ? "in probing" : "", SCIPconsGetName(cons), bnd, SCIPvarGetName(var));
      *result = SCIP_CUTOFF;
      SCIP_CALL( SCIPresetConsAge(scip, cons) );
      return SCIP_OKAY;
   }
   if( tightened )
   {
      SCIPdebugMessage("%s tightened upper bound of variable <%s> in constraint <%s> to %g\n", SCIPinProbing(scip) ? "in probing" : "", SCIPvarGetName(var), SCIPconsGetName(cons), bnd);
      ++*nchgbds;
      *result = SCIP_REDUCEDDOM;
      SCIP_CALL( SCIPresetConsAge(scip, cons) );
   }

   return SCIP_OKAY;
}

/** solves a quadratic equation \f$ a x^2 + b x \in rhs \f$ (with b an interval) and reduces bounds on x or deduces infeasibility if possible
 */
static
SCIP_RETCODE propagateBoundsQuadVar(
   SCIP*                 scip,               /**< SCIP data structure */ 
   SCIP_CONS*            cons,               /**< constraint where we currently propagate */
   SCIP_Real             intervalinfty,      /**< infinity value used in interval operations */
   SCIP_VAR*             var,                /**< variable which bounds with might tighten */
   SCIP_Real             a,                  /**< coefficient in square term */
   SCIP_INTERVAL         b,                  /**< coefficient in linear term */
   SCIP_INTERVAL         rhs,                /**< right hand side of quadratic equation */
   SCIP_RESULT*          result,             /**< result of propagation */
   int*                  nchgbds             /**< buffer where to add number of tightened bounds */
   )
{
   SCIP_INTERVAL newrange;

   assert(scip != NULL);
   assert(cons != NULL);
   assert(var != NULL);
   assert(result != NULL);
   assert(nchgbds != NULL);

   /* compute solution of a*x^2 + b*x \in rhs */
   if( a == 0.0 && SCIPintervalGetInf(b) == 0.0 && SCIPintervalGetSup(b) == 0.0 )
   { /* relatively easy case: 0.0 \in rhs, thus check if infeasible or just redundant */
      if( SCIPintervalGetInf(rhs) > 0.0 || SCIPintervalGetSup(rhs) < 0.0 )
      {
         SCIPdebugMessage("found <%s> infeasible due to domain propagation for quadratic variable <%s>\n", SCIPconsGetName(cons), SCIPvarGetName(var));
         SCIP_CALL( SCIPresetConsAge(scip, cons) );
         *result = SCIP_CUTOFF;
      }
      return SCIP_OKAY;
   }
   else if( SCIPvarGetLbLocal(var) >= 0.0 )
   { 
      SCIP_INTERVAL a_;

      /* need only positive solutions */
      SCIPintervalSet(&a_, a);
      SCIPintervalSolveUnivariateQuadExpressionPositive(intervalinfty, &newrange, a_, b, rhs);
   }
   else if( SCIPvarGetUbLocal(var) <= 0.0 )
   {
      /* need only negative solutions */
      SCIP_INTERVAL a_;
      SCIP_INTERVAL tmp;
      SCIPintervalSet(&a_, a);
      SCIPintervalSetBounds(&tmp, -SCIPintervalGetSup(b), -SCIPintervalGetInf(b));
      SCIPintervalSolveUnivariateQuadExpressionPositive(intervalinfty, &tmp, a_, tmp, rhs);
      if( SCIPintervalIsEmpty(tmp) )
      {
         SCIPdebugMessage("found <%s> infeasible due to domain propagation for quadratic variable <%s>\n", SCIPconsGetName(cons), SCIPvarGetName(var));
         *result = SCIP_CUTOFF;
         SCIP_CALL( SCIPresetConsAge(scip, cons) );
         return SCIP_OKAY;
      }
      SCIPintervalSetBounds(&newrange, -SCIPintervalGetSup(tmp), -SCIPintervalGetInf(tmp));
   }
   else
   {
      /* need both positive and negative solution */
      SCIP_INTERVAL a_;
      SCIPintervalSet(&a_, a);
      SCIPintervalSolveUnivariateQuadExpression(intervalinfty, &newrange, a_, b, rhs);
   }

   /* SCIPdebugMessage("%g x^2 + [%g, %g] x in [%g, %g] -> [%g, %g]\n", a, b.inf, b.sup, rhs.inf, rhs.sup, newrange.inf, newrange.sup); */

   if( SCIPisInfinity(scip, SCIPintervalGetInf(newrange)) || SCIPisInfinity(scip, -SCIPintervalGetSup(newrange)) )
   { /* domain outside [-infty, +infty] -> declare node infeasible */
      SCIPdebugMessage("found <%s> infeasible because propagated domain of quadratic variable <%s> is outside of (-infty, +infty)\n", SCIPconsGetName(cons), SCIPvarGetName(var));
      *result = SCIP_CUTOFF;
      SCIP_CALL( SCIPresetConsAge(scip, cons) );
      return SCIP_OKAY;
   }

   if( SCIPintervalIsEmpty(newrange) )
   {
      SCIPdebugMessage("found <%s> infeasible due to domain propagation for quadratic variable <%s>\n", SCIPconsGetName(cons), SCIPvarGetName(var));
      *result = SCIP_CUTOFF;
      return SCIP_OKAY;
   }

   if( !SCIPisInfinity(scip, -SCIPintervalGetInf(newrange)) )
   {
      SCIP_CALL( propagateBoundsTightenVarLb(scip, cons, intervalinfty, var, SCIPintervalGetInf(newrange), result, nchgbds) );
      if( *result == SCIP_CUTOFF )
         return SCIP_OKAY;
   }

   if( !SCIPisInfinity(scip,  SCIPintervalGetSup(newrange)) )
   {
      SCIP_CALL( propagateBoundsTightenVarUb(scip, cons, intervalinfty, var, SCIPintervalGetSup(newrange), result, nchgbds) );
      if( *result == SCIP_CUTOFF )
         return SCIP_OKAY;
   }

   return SCIP_OKAY;
}

/* the new version below computes potentially tighter bounds, but also always adds a small safety area since it is not implemented roundingsafe,
 * this may be a reason why it gives worse results on one of two instances
 * further, I have only very few instances where one can expect a difference
 */
#ifndef PROPBILINNEW
/** tries to deduce domain reductions for x in xsqrcoef x^2 + xlincoef x + ysqrcoef y^2 + ylincoef y + bilincoef x y \\in rhs
 * NOTE that domain reductions for y are not deduced 
 */
static
SCIP_RETCODE propagateBoundsBilinearTerm(
   SCIP*                 scip,               /**< SCIP data structure */
   SCIP_CONS*            cons,               /**< the constraint, where the bilinear term belongs to */
   SCIP_Real             intervalinfty,      /**< infinity value used in interval operations */
   SCIP_VAR*             x,                  /**< first variable */
   SCIP_Real             xsqrcoef,           /**< square coefficient of x */
   SCIP_Real             xlincoef,           /**< linear coefficient of x */
   SCIP_VAR*             y,                  /**< second variable */
   SCIP_Real             ysqrcoef,           /**< square coefficient of y */
   SCIP_Real             ylincoef,           /**< linear coefficient of y */
   SCIP_Real             bilincoef,          /**< bilinear coefficient of x*y */
   SCIP_INTERVAL         rhs,                /**< right hand side of quadratic equation */
   SCIP_RESULT*          result,             /**< pointer to store result of domain propagation */
   int*                  nchgbds             /**< counter to increment if domain reductions are found */
   )
{
   SCIP_INTERVAL myrhs;
   SCIP_INTERVAL varbnds;
   SCIP_INTERVAL lincoef;

   assert(scip != NULL);
   assert(cons != NULL);
   assert(x != NULL);
   assert(y != NULL);
   assert(x != y);
   assert(result != NULL);
   assert(*result == SCIP_DIDNOTFIND || *result == SCIP_REDUCEDDOM);
   assert(nchgbds != NULL);
   assert(bilincoef != 0.0);

   if( SCIPintervalIsEntire(intervalinfty, rhs) )
      return SCIP_OKAY;

   /* try to find domain reductions for x */
   SCIPintervalSetBounds(&varbnds, MIN(SCIPvarGetLbLocal(y), SCIPvarGetUbLocal(y)), MAX(SCIPvarGetLbLocal(y), SCIPvarGetUbLocal(y)));  /*lint !e666 */

   /* put ysqrcoef*y^2 + ylincoef * y into rhs */
   if( SCIPintervalGetSup(rhs) >= intervalinfty )
   {
      /* if rhs is unbounded by above, it is sufficient to get an upper bound on ysqrcoef*y^2 + ylincoef * y */
      SCIP_ROUNDMODE roundmode;
      SCIP_Real      tmp;

      SCIPintervalSet(&lincoef, ylincoef);
      tmp = SCIPintervalQuadUpperBound(intervalinfty, ysqrcoef, lincoef, varbnds);
      roundmode = SCIPintervalGetRoundingMode();
      SCIPintervalSetRoundingModeDownwards();
      SCIPintervalSetBounds(&myrhs, SCIPintervalGetInf(rhs) - tmp, intervalinfty);
      SCIPintervalSetRoundingMode(roundmode);
   }
   else if( SCIPintervalGetInf(rhs) <= -intervalinfty )
   {
      /* if rhs is unbounded by below, it is sufficient to get a  lower bound on ysqrcoef*y^2 + ylincoef * y */
      SCIP_ROUNDMODE roundmode;
      SCIP_Real      tmp;

      SCIPintervalSet(&lincoef, -ylincoef);
      tmp = -SCIPintervalQuadUpperBound(intervalinfty, -ysqrcoef, lincoef, varbnds);
      roundmode = SCIPintervalGetRoundingMode();
      SCIPintervalSetRoundingModeUpwards();
      SCIPintervalSetBounds(&myrhs, -intervalinfty, SCIPintervalGetSup(rhs) - tmp);
      SCIPintervalSetRoundingMode(roundmode);
   }
   else
   {
      /* if rhs is bounded, we need both bounds on ysqrcoef*y^2 + ylincoef * y */
      SCIP_INTERVAL tmp;

      SCIPintervalSet(&lincoef, ylincoef);
      SCIPintervalQuad(intervalinfty, &tmp, ysqrcoef, lincoef, varbnds);
      SCIPintervalSub(intervalinfty, &myrhs, rhs, tmp);
   }

   /* create equation xsqrcoef * x^2 + (xlincoef + bilincoef * [ylb, yub]) * x \in myrhs */
   SCIPintervalMulScalar(intervalinfty, &lincoef, varbnds, bilincoef);
   SCIPintervalAddScalar(intervalinfty, &lincoef, lincoef, xlincoef);

   /* propagate bounds on x */
   SCIP_CALL( propagateBoundsQuadVar(scip, cons, intervalinfty, x, xsqrcoef, lincoef, myrhs, result, nchgbds) );

   return SCIP_OKAY;
}
#else
/** tries to deduce domain reductions for x in xsqrcoef x^2 + xlincoef x + ysqrcoef y^2 + ylincoef y + bilincoef x y \\in rhs
 * NOTE that domain reductions for y are not deduced
 */
static
SCIP_RETCODE propagateBoundsBilinearTerm(
   SCIP*                 scip,               /**< SCIP data structure */
   SCIP_CONS*            cons,               /**< the constraint, where the bilinear term belongs to */
   SCIP_Real             intervalinfty,      /**< infinity value used in interval operations */
   SCIP_VAR*             x,                  /**< first variable */
   SCIP_Real             xsqrcoef,           /**< square coefficient of x */
   SCIP_Real             xlincoef,           /**< linear coefficient of x */
   SCIP_VAR*             y,                  /**< second variable */
   SCIP_Real             ysqrcoef,           /**< square coefficient of y */
   SCIP_Real             ylincoef,           /**< linear coefficient of y */
   SCIP_Real             bilincoef,          /**< bilinear coefficient of x*y */
   SCIP_INTERVAL         rhs,                /**< right hand side of quadratic equation */
   SCIP_RESULT*          result,             /**< pointer to store result of domain propagation */
   int*                  nchgbds             /**< counter to increment if domain reductions are found */
   )
{
   SCIP_INTERVAL xbnds;
   SCIP_INTERVAL ybnds;

   assert(scip != NULL);
   assert(cons != NULL);
   assert(x != NULL);
   assert(y != NULL);
   assert(x != y);
   assert(result != NULL);
   assert(*result == SCIP_DIDNOTFIND || *result == SCIP_REDUCEDDOM);
   assert(nchgbds != NULL);
   assert(bilincoef != 0.0);

   if( SCIPintervalIsEntire(intervalinfty, rhs) )
      return SCIP_OKAY;

   SCIPintervalSetBounds(&xbnds,
      -infty2infty(SCIPinfinity(scip), intervalinfty, -MIN(SCIPvarGetLbLocal(x), SCIPvarGetUbLocal(x))),   /*lint !e666*/
      +infty2infty(SCIPinfinity(scip), intervalinfty,  MAX(SCIPvarGetLbLocal(x), SCIPvarGetUbLocal(x))));  /*lint !e666*/
   SCIPintervalSetBounds(&ybnds,
      -infty2infty(SCIPinfinity(scip), intervalinfty, -MIN(SCIPvarGetLbLocal(y), SCIPvarGetUbLocal(y))),   /*lint !e666*/
      +infty2infty(SCIPinfinity(scip), intervalinfty,  MAX(SCIPvarGetLbLocal(y), SCIPvarGetUbLocal(y))));  /*lint !e666*/

   /* try to find domain reductions for x */
   SCIPintervalSolveBivariateQuadExpressionAllScalar(intervalinfty, &xbnds, xsqrcoef, ysqrcoef, bilincoef, xlincoef, ylincoef, rhs, xbnds, ybnds);

   if( SCIPintervalIsEmpty(xbnds) )
   {
      SCIPdebugMessage("found <%s> infeasible due to domain propagation for quadratic variable <%s>\n", SCIPconsGetName(cons), SCIPvarGetName(x));
      *result = SCIP_CUTOFF;
      return SCIP_OKAY;
   }

   if( !SCIPisInfinity(scip, -SCIPintervalGetInf(xbnds)) )
   {
      SCIP_CALL( propagateBoundsTightenVarLb(scip, cons, intervalinfty, x, SCIPintervalGetInf(xbnds), result, nchgbds) );
      if( *result == SCIP_CUTOFF )
         return SCIP_OKAY;
   }

   if( !SCIPisInfinity(scip,  SCIPintervalGetSup(xbnds)) )
   {
      SCIP_CALL( propagateBoundsTightenVarUb(scip, cons, intervalinfty, x, SCIPintervalGetSup(xbnds), result, nchgbds) );
      if( *result == SCIP_CUTOFF )
         return SCIP_OKAY;
   }

   return SCIP_OKAY;
}
#endif

/** computes the minimal and maximal activity for the quadratic part in a constraint data
 *  only sums up terms that contribute finite values
 *  gives the number of terms that contribute infinite values
 *  only computes those activities where the corresponding side of the constraint is finite
 */
static
void propagateBoundsGetQuadActivity(
   SCIP*                 scip,               /**< SCIP data structure */
   SCIP_CONSDATA*        consdata,           /**< constraint data */
   SCIP_Real             intervalinfty,      /**< infinity value used in interval operations */
   SCIP_Real*            minquadactivity,    /**< minimal activity of quadratic variable terms where only terms with finite minimal activity contribute */
   SCIP_Real*            maxquadactivity,    /**< maximal activity of quadratic variable terms where only terms with finite maximal activity contribute */
   int*                  minactivityinf,     /**< number of quadratic variables that contribute -infinity to minimal activity */
   int*                  maxactivityinf,     /**< number of quadratic variables that contribute +infinity to maximal activity */
   SCIP_INTERVAL*        quadactcontr        /**< contribution of each quadratic variables to quadactivity */
   )
{  /*lint --e{666}*/
   SCIP_ROUNDMODE prevroundmode;
   int       i;
   int       j;
   int       k;
   SCIP_INTERVAL tmp;
   SCIP_Real bnd;
   SCIP_INTERVAL xrng;
   SCIP_INTERVAL lincoef;

   assert(scip != NULL);
   assert(consdata != NULL);
   assert(minquadactivity != NULL);
   assert(maxquadactivity != NULL);
   assert(minactivityinf != NULL);
   assert(maxactivityinf != NULL);
   assert(quadactcontr != NULL);

   /* if lhs is -infinite, then we do not compute a maximal activity, so we set it to  infinity
    * if rhs is  infinite, then we do not compute a minimal activity, so we set it to -infinity
    */
   *minquadactivity = SCIPisInfinity(scip,  consdata->rhs) ? -intervalinfty : 0.0;
   *maxquadactivity = SCIPisInfinity(scip, -consdata->lhs) ?  intervalinfty : 0.0;

   *minactivityinf = 0;
   *maxactivityinf = 0;

   if( consdata->nquadvars == 0 )
   {
      SCIPintervalSet(&consdata->quadactivitybounds, 0.0); 
      return;
   }

   for( i = 0; i < consdata->nquadvars; ++i )
   {
      /* there should be no quadratic variables fixed at -/+ infinity due to our locks */
      assert(!SCIPisInfinity(scip,  SCIPvarGetLbLocal(consdata->quadvarterms[i].var)));
      assert(!SCIPisInfinity(scip, -SCIPvarGetUbLocal(consdata->quadvarterms[i].var)));

      SCIPintervalSetBounds(&quadactcontr[i], -intervalinfty, intervalinfty);

      SCIPintervalSetBounds(&xrng,
         -infty2infty(SCIPinfinity(scip), intervalinfty, -MIN(SCIPvarGetLbLocal(consdata->quadvarterms[i].var), SCIPvarGetUbLocal(consdata->quadvarterms[i].var))),
         +infty2infty(SCIPinfinity(scip), intervalinfty,  MAX(SCIPvarGetLbLocal(consdata->quadvarterms[i].var), SCIPvarGetUbLocal(consdata->quadvarterms[i].var))));

      SCIPintervalSet(&lincoef, consdata->quadvarterms[i].lincoef);
      for( j = 0; j < consdata->quadvarterms[i].nadjbilin; ++j )
      {
         k = consdata->quadvarterms[i].adjbilin[j];
         if( consdata->bilinterms[k].var1 != consdata->quadvarterms[i].var )
            continue; /* handle this term later */

         SCIPintervalSetBounds(&tmp, 
            -infty2infty(SCIPinfinity(scip), intervalinfty, -MIN(SCIPvarGetLbLocal(consdata->bilinterms[k].var2), SCIPvarGetUbLocal(consdata->bilinterms[k].var2))),
            +infty2infty(SCIPinfinity(scip), intervalinfty,  MAX(SCIPvarGetLbLocal(consdata->bilinterms[k].var2), SCIPvarGetUbLocal(consdata->bilinterms[k].var2))));
         SCIPintervalMulScalar(intervalinfty, &tmp, tmp, consdata->bilinterms[k].coef);
         SCIPintervalAdd(intervalinfty, &lincoef, lincoef, tmp);
      }

      if( !SCIPisInfinity(scip, -consdata->lhs) )
      {
         /* compute maximal activity only if there is a finite left hand side */
         bnd = SCIPintervalQuadUpperBound(intervalinfty, consdata->quadvarterms[i].sqrcoef, lincoef, xrng);
         if( SCIPisInfinity(scip,  bnd) )
         {
            ++*maxactivityinf;
         }
         else if( SCIPisInfinity(scip, -bnd) )
         {
            /* if maximal activity is below value for -infinity, let's take -1e10 as upper bound on maximal activity
             * @todo Something better?
             */
            bnd = -sqrt(SCIPinfinity(scip));
            *maxquadactivity += bnd;
            quadactcontr[i].sup = bnd;
         }
         else
         {
            prevroundmode = SCIPintervalGetRoundingMode();
            SCIPintervalSetRoundingModeUpwards();
            *maxquadactivity += bnd;
            SCIPintervalSetRoundingMode(prevroundmode);
            quadactcontr[i].sup = bnd;
         }
      }

      if( !SCIPisInfinity(scip,  consdata->rhs) )
      {
         /* compute minimal activity only if there is a finite right hand side */
         SCIPintervalSetBounds(&lincoef, -SCIPintervalGetSup(lincoef), -SCIPintervalGetInf(lincoef));
         bnd = -SCIPintervalQuadUpperBound(intervalinfty, -consdata->quadvarterms[i].sqrcoef, lincoef, xrng);

         if( SCIPisInfinity(scip, -bnd) )
         {
            ++*minactivityinf;
         }
         else if( SCIPisInfinity(scip, bnd) )
         {
            /* if minimal activity is above value for infinity, let's take 1e10 as lower bound on minimal activity
             * @todo Something better?
             */
            bnd = sqrt(SCIPinfinity(scip));
            *minquadactivity += bnd;
            quadactcontr[i].inf = bnd;
         }
         else
         {
            prevroundmode = SCIPintervalGetRoundingMode();
            SCIPintervalSetRoundingModeDownwards();
            *minquadactivity += bnd;
            SCIPintervalSetRoundingMode(prevroundmode);
            quadactcontr[i].inf = bnd;
         }
      }

   }

   SCIPintervalSetBounds(&consdata->quadactivitybounds,
      (*minactivityinf > 0 ? -intervalinfty : *minquadactivity),
      (*maxactivityinf > 0 ?  intervalinfty : *maxquadactivity));
   assert(!SCIPintervalIsEmpty(consdata->quadactivitybounds));
}

/** propagates bounds on a quadratic constraint */
static
SCIP_RETCODE propagateBoundsCons(
   SCIP*                 scip,               /**< SCIP data structure */
   SCIP_CONSHDLR*        conshdlr,           /**< constraint handler */
   SCIP_CONS*            cons,               /**< constraint to process */
   SCIP_RESULT*          result,             /**< pointer to store the result of the propagation call */
   int*                  nchgbds,            /**< buffer where to add the the number of changed bounds */
   SCIP_Bool*            redundant           /**< buffer where to store whether constraint has been found to be redundant */
   )
{  /*lint --e{666}*/
   SCIP_CONSDATA*     consdata;
   SCIP_INTERVAL      consbounds;    /* lower and upper bounds of constraint */
   SCIP_INTERVAL      consactivity;  /* activity of linear plus quadratic part */
   SCIP_Real          intervalinfty; /* infinity used for interval computation */  
   SCIP_Real          minquadactivity; /* lower bound on finite activities of quadratic part */
   SCIP_Real          maxquadactivity; /* upper bound on finite activities of quadratic part */
   int                quadminactinf; /* number of quadratic variables that contribute -infinity to minimal activity of quadratic term */
   int                quadmaxactinf; /* number of quadratic variables that contribute +infinity to maximal activity of quadratic term */
   SCIP_INTERVAL*     quadactcontr;  /* contribution of each quadratic variable term to quadactivity */

   SCIP_VAR*          var;
   SCIP_INTERVAL      rhs;           /* right hand side of quadratic equation */
   SCIP_INTERVAL      tmp;
   SCIP_ROUNDMODE     roundmode;
   SCIP_Real          bnd;
   int                i;

   assert(scip != NULL);
   assert(conshdlr != NULL);
   assert(cons != NULL);
   assert(result != NULL);
   assert(nchgbds != NULL);
   assert(redundant != NULL);

   consdata = SCIPconsGetData(cons);
   assert(consdata != NULL);

   *result = SCIP_DIDNOTRUN;
   *redundant = FALSE;

   if( consdata->ispropagated )
      return SCIP_OKAY;

   *result = SCIP_DIDNOTFIND;

   intervalinfty = 1000 * SCIPinfinity(scip) * SCIPinfinity(scip);

   quadactcontr = NULL;
   quadminactinf = -1;
   quadmaxactinf = -1;

   SCIPdebugMessage("start domain propagation for constraint <%s>\n", SCIPconsGetName(cons));

   consdata->ispropagated = TRUE;

   /* make sure we have activity of linear term and that they are consistent */
   consdataUpdateLinearActivity(scip, consdata, intervalinfty);
   assert(consdata->minlinactivity != SCIP_INVALID);  /*lint !e777 */
   assert(consdata->maxlinactivity != SCIP_INVALID);  /*lint !e777 */
   assert(consdata->minlinactivityinf >= 0);
   assert(consdata->maxlinactivityinf >= 0);

   /* sort quadratic variable terms, in case we need to search for terms occuring in bilinear terms later
    * we sort here already, since we rely on a constant variable order during this method
    */
   if( consdata->nbilinterms > 0 )
   {
      SCIP_CALL( consdataSortQuadVarTerms(scip, consdata) );
   }

   /* compute activity of quad term part, if not up to date
    * in that case, we also collect the contribution of each quad var term for later */
   if( SCIPintervalIsEmpty(consdata->quadactivitybounds) )
   {
      SCIP_CALL( SCIPallocBufferArray(scip, &quadactcontr, consdata->nquadvars) );
      propagateBoundsGetQuadActivity(scip, consdata, intervalinfty, &minquadactivity, &maxquadactivity, &quadminactinf, &quadmaxactinf, quadactcontr);
      assert(!SCIPintervalIsEmpty(consdata->quadactivitybounds));
   }

   SCIPdebugMessage("linear activity: [%g, %g]   quadratic activity: [%g, %g]\n",
      (consdata->minlinactivityinf > 0 ? -SCIPinfinity(scip) : consdata->minlinactivity),
      (consdata->maxlinactivityinf > 0 ?  SCIPinfinity(scip) : consdata->maxlinactivity),
      consdata->quadactivitybounds.inf, consdata->quadactivitybounds.sup);

   /* extend constraint bounds by epsilon to avoid some numerical difficulties */
   SCIPintervalSetBounds(&consbounds,
      -infty2infty(SCIPinfinity(scip), intervalinfty, -consdata->lhs+SCIPepsilon(scip)),
      +infty2infty(SCIPinfinity(scip), intervalinfty,  consdata->rhs+SCIPepsilon(scip)));

   /* check redundancy and infeasibility */
   SCIPintervalSetBounds(&consactivity, consdata->minlinactivityinf > 0 ? -intervalinfty : consdata->minlinactivity, consdata->maxlinactivityinf > 0 ? intervalinfty : consdata->maxlinactivity);
   SCIPintervalAdd(intervalinfty, &consactivity, consactivity, consdata->quadactivitybounds);
   if( SCIPintervalIsSubsetEQ(intervalinfty, consactivity, consbounds) )
   {
      SCIPdebugMessage("found constraint <%s> to be redundant: sides: [%g, %g], activity: [%g, %g]\n",
         SCIPconsGetName(cons), consdata->lhs, consdata->rhs, SCIPintervalGetInf(consactivity), SCIPintervalGetSup(consactivity));
      *redundant = TRUE;
      goto CLEANUP;
   }

   /* was SCIPintervalAreDisjoint(consbounds, consactivity), but that would allow violations up to eps only
    * we need to decide feasibility w.r.t. feastol (but still want to propagate w.r.t. eps)
    */
   if( SCIPisFeasGT(scip, consbounds.inf, consactivity.sup) || SCIPisFeasLT(scip, consbounds.sup, consactivity.inf) )
   {
      SCIPdebugMessage("found constraint <%s> to be infeasible; sides: [%g, %g], activity: [%g, %g], infeas: %g\n",
         SCIPconsGetName(cons), consdata->lhs, consdata->rhs, SCIPintervalGetInf(consactivity), SCIPintervalGetSup(consactivity),
         MAX(consdata->lhs - SCIPintervalGetSup(consactivity), SCIPintervalGetInf(consactivity) - consdata->rhs));
      *result = SCIP_CUTOFF;
      goto CLEANUP;
   }

   /* propagate linear part \in rhs = consbounds - quadactivity (use the one from consdata, since that includes infinities) */
   SCIPintervalSub(intervalinfty, &rhs, consbounds, consdata->quadactivitybounds);
   if( !SCIPintervalIsEntire(intervalinfty, rhs) )
   {
      SCIP_Real coef;

      for( i = 0; i < consdata->nlinvars; ++i )
      {
         coef = consdata->lincoefs[i];
         var  = consdata->linvars[i];

         /* skip fixed variables
          * @todo is that a good or a bad idea?
          *   we can't expect much more tightening, but may detect infeasiblity, but shouldn't the check on the constraints activity detect that?
          */
         if( SCIPisEQ(scip, SCIPvarGetLbLocal(var), SCIPvarGetUbLocal(var)) )
            continue;

         if( coef > 0.0 )
         {
            if( SCIPintervalGetSup(rhs) < intervalinfty )
            {
               assert(consdata->minlinactivity != SCIP_INVALID);  /*lint !e777 */
               /* try to tighten the upper bound on var x */
               if( consdata->minlinactivityinf == 0 )
               {
                  assert(!SCIPisInfinity(scip, -SCIPvarGetLbLocal(var)));
                  /* tighten upper bound on x to (rhs.sup - (minlinactivity - coef * xlb)) / coef */
                  roundmode = SCIPintervalGetRoundingMode();
                  SCIPintervalSetRoundingModeUpwards();
                  bnd  = SCIPintervalGetSup(rhs);
                  bnd -= consdata->minlinactivity;
                  bnd += coef * SCIPvarGetLbLocal(var);
                  bnd /= coef;
                  SCIPintervalSetRoundingMode(roundmode);
                  SCIP_CALL( propagateBoundsTightenVarUb(scip, cons, intervalinfty, var, bnd, result, nchgbds) );
                  if( *result == SCIP_CUTOFF )
                     break;
               }
               else if( consdata->minlinactivityinf == 1 && SCIPisInfinity(scip, -SCIPvarGetLbLocal(var)) )
               {
                  /* x was the variable that made the minimal linear activity equal -infinity, so
                   * we tighten upper bound on x to just (rhs.sup - minlinactivity) / coef */
                  roundmode = SCIPintervalGetRoundingMode();
                  SCIPintervalSetRoundingModeUpwards();
                  bnd  = SCIPintervalGetSup(rhs);
                  bnd -= consdata->minlinactivity;
                  bnd /= coef;
                  SCIPintervalSetRoundingMode(roundmode);
                  SCIP_CALL( propagateBoundsTightenVarUb(scip, cons, intervalinfty, var, bnd, result, nchgbds) );
                  if( *result == SCIP_CUTOFF )
                     break;
               }
               /* otherwise the minimal activity is -infinity and x is not solely responsible for this */
            }

            if( SCIPintervalGetInf(rhs) > -intervalinfty )
            {
               assert(consdata->maxlinactivity != SCIP_INVALID);  /*lint !e777 */
               /* try to tighten the lower bound on var x */
               if( consdata->maxlinactivityinf == 0 )
               {
                  assert(!SCIPisInfinity(scip, SCIPvarGetUbLocal(var)));
                  /* tighten lower bound on x to (rhs.inf - (maxlinactivity - coef * xub)) / coef */
                  roundmode = SCIPintervalGetRoundingMode();
                  SCIPintervalSetRoundingModeDownwards();
                  bnd  = SCIPintervalGetInf(rhs);
                  bnd -= consdata->maxlinactivity;
                  bnd += coef * SCIPvarGetUbLocal(var);
                  bnd /= coef;
                  SCIPintervalSetRoundingMode(roundmode);
                  SCIP_CALL( propagateBoundsTightenVarLb(scip, cons, intervalinfty, var, bnd, result, nchgbds) );
                  if( *result == SCIP_CUTOFF )
                     break;
               }
               else if( consdata->maxlinactivityinf == 1 && SCIPisInfinity(scip, SCIPvarGetUbLocal(var)) )
               {
                  /* x was the variable that made the maximal linear activity equal infinity, so
                   * we tighten upper bound on x to just (rhs.inf - maxlinactivity) / coef */
                  roundmode = SCIPintervalGetRoundingMode();
                  SCIPintervalSetRoundingModeDownwards();
                  bnd  = SCIPintervalGetInf(rhs);
                  bnd -= consdata->maxlinactivity;
                  bnd /= coef;
                  SCIPintervalSetRoundingMode(roundmode);
                  SCIP_CALL( propagateBoundsTightenVarLb(scip, cons, intervalinfty, var, bnd, result, nchgbds) );
                  if( *result == SCIP_CUTOFF )
                     break;
               }
               /* otherwise the maximal activity is +infinity and x is not solely responsible for this */
            }
         }
         else
         {
            assert(coef < 0.0 );
            if( SCIPintervalGetInf(rhs) > -intervalinfty )
            {
               assert(consdata->maxlinactivity != SCIP_INVALID);  /*lint !e777 */
               /* try to tighten the upper bound on var x */
               if( consdata->maxlinactivityinf == 0 )
               {
                  assert(!SCIPisInfinity(scip, SCIPvarGetLbLocal(var)));
                  /* compute upper bound on x to (maxlinactivity - coef * xlb) - rhs.inf / (-coef) */
                  roundmode = SCIPintervalGetRoundingMode();
                  SCIPintervalSetRoundingModeUpwards();
                  bnd  = consdata->maxlinactivity;
                  bnd += (-coef) * SCIPvarGetLbLocal(var);
                  bnd -= SCIPintervalGetInf(rhs);
                  bnd /= (-coef);
                  SCIPintervalSetRoundingMode(roundmode);
                  SCIP_CALL( propagateBoundsTightenVarUb(scip, cons, intervalinfty, var, bnd, result, nchgbds) );
                  if( *result == SCIP_CUTOFF )
                     break;
               }
               else if( consdata->maxlinactivityinf == 1 && SCIPisInfinity(scip, -SCIPvarGetLbLocal(var)) )
               {
                  /* x was the variable that made the maximal linear activity equal infinity, so
                   * we tighten upper bound on x to just (maxlinactivity - rhs.inf) / (-coef) */
                  roundmode = SCIPintervalGetRoundingMode();
                  SCIPintervalSetRoundingModeUpwards();
                  bnd  = consdata->maxlinactivity;
                  bnd -= SCIPintervalGetInf(rhs);
                  bnd /= (-coef);
                  SCIPintervalSetRoundingMode(roundmode);
                  SCIP_CALL( propagateBoundsTightenVarUb(scip, cons, intervalinfty, var, bnd, result, nchgbds) );
                  if( *result == SCIP_CUTOFF )
                     break;
               }
               /* otherwise the maximal activity is infinity and x is not solely responsible for this */
            }

            if( SCIPintervalGetSup(rhs) < intervalinfty )
            {
               assert(consdata->minlinactivity != SCIP_INVALID);  /*lint !e777 */
               /* try to tighten the lower bound on var x */
               if( consdata->minlinactivityinf == 0 )
               {
                  assert(!SCIPisInfinity(scip, SCIPvarGetUbLocal(var)));
                  /* compute lower bound on x to (minlinactivity - coef * xub) - rhs.sup / (-coef) */
                  roundmode = SCIPintervalGetRoundingMode();
                  SCIPintervalSetRoundingModeDownwards();
                  bnd  = consdata->minlinactivity;
                  bnd += (-coef) * SCIPvarGetUbLocal(var);
                  bnd -= SCIPintervalGetSup(rhs);
                  bnd /= (-coef);
                  SCIPintervalSetRoundingMode(roundmode);
                  SCIP_CALL( propagateBoundsTightenVarLb(scip, cons, intervalinfty, var, bnd, result, nchgbds) );
                  if( *result == SCIP_CUTOFF )
                     break;
               }
               else if( consdata->minlinactivityinf == 1 && SCIPisInfinity(scip, SCIPvarGetUbLocal(var)) )
               {
                  /* x was the variable that made the maximal linear activity equal -infinity, so
                   * we tighten lower bound on x to just (minlinactivity - rhs.sup) / (-coef) */
                  roundmode = SCIPintervalGetRoundingMode();
                  SCIPintervalSetRoundingModeDownwards();
                  bnd  = consdata->minlinactivity;
                  bnd -= SCIPintervalGetSup(rhs);
                  bnd /= (-coef);
                  SCIPintervalSetRoundingMode(roundmode);
                  SCIP_CALL( propagateBoundsTightenVarLb(scip, cons, intervalinfty, var, bnd, result, nchgbds) );
                  if( *result == SCIP_CUTOFF )
                     break;
               }
               /* otherwise the minimal activity is -infinity and x is not solely responsible for this */
            }
         }
      }
      if( *result == SCIP_CUTOFF )
         goto CLEANUP;
   }

   /* propagate quadratic part \in rhs = consbounds - linactivity */
   assert(consdata->minlinactivity != SCIP_INVALID);  /*lint !e777 */
   assert(consdata->maxlinactivity != SCIP_INVALID);  /*lint !e777 */
   consdataUpdateLinearActivity(scip, consdata, intervalinfty); /* make sure, activities of linear part did not become invalid by above bound changes, if any */
   assert(consdata->minlinactivityinf > 0 || consdata->maxlinactivityinf > 0 || consdata->minlinactivity <= consdata->maxlinactivity);
   SCIPintervalSetBounds(&tmp,
      (consdata->minlinactivityinf > 0 ? -intervalinfty : consdata->minlinactivity),
      (consdata->maxlinactivityinf > 0 ?  intervalinfty : consdata->maxlinactivity));
   SCIPintervalSub(intervalinfty, &rhs, consbounds, tmp);
   if( !SCIPintervalIsEntire(intervalinfty, rhs) )
   {
      if( consdata->nquadvars == 1 )
      {
         /* quadratic part is just a*x^2+b*x -> a common case that we treat directly */
         SCIP_INTERVAL lincoef;    /* linear coefficient of quadratic equation */

         assert(consdata->nbilinterms == 0);

         var = consdata->quadvarterms[0].var;
         SCIPintervalSet(&lincoef, consdata->quadvarterms[0].lincoef);

         /* propagate a*x^2 + b*x \in rhs */
         SCIP_CALL( propagateBoundsQuadVar(scip, cons, intervalinfty, var, consdata->quadvarterms[0].sqrcoef, lincoef, rhs, result, nchgbds) );
      }
      else if( consdata->nbilinterms == 1 && consdata->nquadvars == 2 )
      {
         /* quadratic part is just ax*x^2+bx*x + ay*y^2+by*y + c*xy -> a common case that we treat directly */
         assert(consdata->bilinterms[0].var1 == consdata->quadvarterms[0].var || consdata->bilinterms[0].var1 == consdata->quadvarterms[1].var);
         assert(consdata->bilinterms[0].var2 == consdata->quadvarterms[0].var || consdata->bilinterms[0].var2 == consdata->quadvarterms[1].var);

         /* find domain reductions for x from a_x x^2 + b_x x + a_y y^2 + b_y y + c x y \in rhs */
         SCIP_CALL( propagateBoundsBilinearTerm(scip, cons, intervalinfty,
               consdata->quadvarterms[0].var, consdata->quadvarterms[0].sqrcoef, consdata->quadvarterms[0].lincoef,
               consdata->quadvarterms[1].var, consdata->quadvarterms[1].sqrcoef, consdata->quadvarterms[1].lincoef,
               consdata->bilinterms[0].coef,
               rhs, result, nchgbds) );
         if( *result != SCIP_CUTOFF )
         {
            /* find domain reductions for y from a_x x^2 + b_x x + a_y y^2 + b_y y + c x y \in rhs */
            SCIP_CALL( propagateBoundsBilinearTerm(scip, cons, intervalinfty,
                  consdata->quadvarterms[1].var, consdata->quadvarterms[1].sqrcoef, consdata->quadvarterms[1].lincoef,
                  consdata->quadvarterms[0].var, consdata->quadvarterms[0].sqrcoef, consdata->quadvarterms[0].lincoef,
                  consdata->bilinterms[0].coef,
                  rhs, result, nchgbds) );
         }
      }
      else
      {
         /* general case */

         /* compute "advanced" information on quad var term activities, if not up-to-date */
         if( quadminactinf == -1  )
         {
            assert(quadactcontr == NULL);
            SCIP_CALL( SCIPallocBufferArray(scip, &quadactcontr, consdata->nquadvars) );
            propagateBoundsGetQuadActivity(scip, consdata, intervalinfty, &minquadactivity, &maxquadactivity, &quadminactinf, &quadmaxactinf, quadactcontr);
         }
         assert(quadactcontr != NULL);
         assert(quadminactinf >= 0);
         assert(quadmaxactinf >= 0);

         /* if the quad activities are not hopelessly unbounded on useful sides, try to deduce domain reductions on quad vars */
         if( (SCIPintervalGetSup(rhs) <  intervalinfty && quadminactinf <= 1) ||
            ( SCIPintervalGetInf(rhs) > -intervalinfty && quadmaxactinf <= 1) )
         {
            SCIP_INTERVAL lincoef;
            SCIP_INTERVAL rhs2;
            int j;
            int k;

            for( i = 0; i < consdata->nquadvars; ++i )
            {
               var = consdata->quadvarterms[i].var;

               /* skip fixed variables
                * @todo is that a good or a bad idea?
                *   we can't expect much more tightening, but may detect infeasiblity, but shouldn't the check on the constraints activity detect that?
                */
               if( SCIPisEQ(scip, SCIPvarGetLbLocal(var), SCIPvarGetUbLocal(var)) )
                  continue;

               /* compute rhs2 such that we can propagate quadvarterm(x_i) \in rhs2 */

               /* setup rhs2.sup = rhs.sup - (quadactivity.inf - quadactcontr[i].inf), if everything were finite
                * if only quadactcontr[i].inf is infinite (i.e., the other i are all finite), we just get rhs2.sup = rhs.sup
                * otherwise we get rhs2.sup = infinity */
               if( SCIPintervalGetSup(rhs) < intervalinfty )
               {
                  if( quadminactinf == 0 || (quadminactinf == 1 && SCIPintervalGetInf(quadactcontr[i]) <= -intervalinfty) )
                  {
                     roundmode = SCIPintervalGetRoundingMode();
                     SCIPintervalSetRoundingModeUpwards();
                     rhs2.sup = rhs.sup - minquadactivity;  /*lint !e644*/
                     /* if the residual quad min activity w.r.t. quad var term i is finite and nonzero, so add it to right hand side */
                     if( quadminactinf == 0 && SCIPintervalGetInf(quadactcontr[i]) != 0.0 )
                        rhs2.sup += SCIPintervalGetInf(quadactcontr[i]);
                     SCIPintervalSetRoundingMode(roundmode);
                  }
                  else
                  {
                     /* there are either >= 2 quad var terms contributing -infinity, or there is one which is not i */
                     rhs2.sup = intervalinfty;
                  }
               }
               else
               {
                  rhs2.sup = intervalinfty;
               }

               /* setup rhs2.inf = rhs.inf - (quadactivity.sup - quadactcontr[i].sup), see also above */
               if( SCIPintervalGetInf(rhs) > -intervalinfty )
               {
                  if( quadmaxactinf == 0 || (quadmaxactinf == 1 && SCIPintervalGetSup(quadactcontr[i]) >= intervalinfty) )
                  {
                     roundmode = SCIPintervalGetRoundingMode();
                     SCIPintervalSetRoundingModeDownwards();
                     rhs2.inf = rhs.inf - maxquadactivity;  /*lint !e644*/
                     /* if the residual quad max activity w.r.t. quad var term i is finite and nonzero, so add it to right hand side */
                     if( quadmaxactinf == 0 && SCIPintervalGetSup(quadactcontr[i]) != 0.0 )
                        rhs2.inf += SCIPintervalGetSup(quadactcontr[i]);
                     SCIPintervalSetRoundingMode(roundmode);
                  }
                  else
                  {
                     /* there are either >= 2 quad var terms contributing infinity, or there is one which is not i */
                     rhs2.inf = -intervalinfty;
                  }
               }
               else
               {
                  rhs2.inf = -intervalinfty;
               }
               assert(!SCIPintervalIsEmpty(rhs2));

               /* if rhs2 is entire, then there is nothing we could propagate */
               if( SCIPintervalIsEntire(intervalinfty, rhs2) )
                  continue;

               /* assemble linear coefficient for quad equation a*x^2 + b*x \in rhs2 */
               SCIPintervalSet(&lincoef, consdata->quadvarterms[i].lincoef);
               for( j = 0; j < consdata->quadvarterms[i].nadjbilin; ++j )
               {
                  k = consdata->quadvarterms[i].adjbilin[j];
#if 1
                  if( consdata->bilinterms[k].var1 == var )
                  {
                     /* bilinear term k contributes to the activity of quad var term i, so just add bounds to linear coef */
                     SCIPintervalSetBounds(&tmp,
                        -infty2infty(SCIPinfinity(scip), intervalinfty, -MIN(SCIPvarGetLbLocal(consdata->bilinterms[k].var2), SCIPvarGetUbLocal(consdata->bilinterms[k].var2))),
                        +infty2infty(SCIPinfinity(scip), intervalinfty,  MAX(SCIPvarGetLbLocal(consdata->bilinterms[k].var2), SCIPvarGetUbLocal(consdata->bilinterms[k].var2))));
                     SCIPintervalMulScalar(intervalinfty, &tmp, tmp, consdata->bilinterms[k].coef);
                     SCIPintervalAdd(intervalinfty, &lincoef, lincoef, tmp);

                  }
                  else
                  {
                     /* bilinear term k does not contribute to the activity of quad var term i
                      * so bounds on term k are contained in rhs2
                      * if they are finite, we try to remove them from rhs2 and update lincoef instead
                      * if the bounds on bilinear term k as added to rhs2 are old due to recent bound tightening, we may not do best possible, but still correct
                      * HOWEVER: when computing rhs2, we may not just have added the bounds for the bilinear term, but for the associated quadratic term
                      *   for this complete term, we used SCIPintervalQuad to compute the bounds
                      *   since we do not want to repeat a call to SCIPintervalQuad for that quadratic term with bilinear term k removed,
                      *   we only remove the bounds for the bilinear term k from rhs2 if the associated quadratic term consists only of this bilinear term,
                      *   i.e., the quadratic term corresponding to var1 should be only var1*var2, but have no square or linear coefs or other bilinear terms
                      *   (for efficiency reasons, we check here only if there are any other bilinear terms than var1*var2 associated with var1, even if they are not associated with the quad var term for var1)
                      */
                     SCIP_INTERVAL me;
                     SCIP_INTERVAL bilinbounds;
                     int otherpos;

                     assert(consdata->bilinterms[k].var2 == var);

                     assert(consdata->quadvarssorted);
                     SCIP_CALL( consdataFindQuadVarTerm(scip, consdata, consdata->bilinterms[k].var1, &otherpos) );
                     assert(otherpos >= 0);
                     assert(consdata->quadvarterms[otherpos].var == consdata->bilinterms[k].var1);

                     if( (consdata->quadvarterms[otherpos].sqrcoef != 0.0) || consdata->quadvarterms[otherpos].lincoef != 0.0 || consdata->quadvarterms[otherpos].nadjbilin > 1 )
                        continue;

                     /* set tmp to bounds of other variable and multiply with bilin coef */
                     SCIPintervalSetBounds(&tmp,
                        -infty2infty(SCIPinfinity(scip), intervalinfty, -MIN(SCIPvarGetLbLocal(consdata->bilinterms[k].var1), SCIPvarGetUbLocal(consdata->bilinterms[k].var1))),
                        +infty2infty(SCIPinfinity(scip), intervalinfty,  MAX(SCIPvarGetLbLocal(consdata->bilinterms[k].var1), SCIPvarGetUbLocal(consdata->bilinterms[k].var1))));
                     SCIPintervalMulScalar(intervalinfty, &tmp, tmp, consdata->bilinterms[k].coef);

                     /* set me to bounds of i'th variable */
                     SCIPintervalSetBounds(&me,
                        -infty2infty(SCIPinfinity(scip), intervalinfty, -MIN(SCIPvarGetLbLocal(consdata->bilinterms[k].var2), SCIPvarGetUbLocal(consdata->bilinterms[k].var2))),
                        +infty2infty(SCIPinfinity(scip), intervalinfty,  MAX(SCIPvarGetLbLocal(consdata->bilinterms[k].var2), SCIPvarGetUbLocal(consdata->bilinterms[k].var2))));

                     /* remove me*tmp from rhs2 */

                     roundmode = SCIPintervalGetRoundingMode();

                     if( rhs2.inf > -intervalinfty )
                     {
                        /* need upward rounding for SCIPintervalMulSup */
                        SCIPintervalSetRoundingModeUpwards();
                        SCIPintervalMulSup(intervalinfty, &bilinbounds, me, tmp);
                        /* rhs2.inf += bilinbounds.sup, but we are in upward rounding */
                        if( bilinbounds.sup < intervalinfty )
                           rhs2.inf = SCIPintervalNegateReal(SCIPintervalNegateReal(rhs2.inf) - bilinbounds.sup);
                     }

                     if( rhs2.sup <  intervalinfty )
                     {
                        /* need downward rounding for SCIPintervalMulInf */
                        SCIPintervalSetRoundingModeDownwards();
                        SCIPintervalMulInf(intervalinfty, &bilinbounds, me, tmp);
                        /* rhs2.sup += bilinbounds.inf, but we are in downward rounding */
                        if( bilinbounds.inf > -intervalinfty )
                           rhs2.sup = SCIPintervalNegateReal(SCIPintervalNegateReal(rhs2.sup) - bilinbounds.inf);
                     }

                     SCIPintervalSetRoundingMode(roundmode);

                     /* add tmp to lincoef */
                     SCIPintervalAdd(intervalinfty, &lincoef, lincoef, tmp);
                  }
#else
                  if( consdata->bilinterms[k].var1 != var )
                     continue; /* this term does not contribute to the activity of quad var term i */

                  SCIPintervalSetBounds(&tmp,
                     -infty2infty(SCIPinfinity(scip), intervalinfty, -MIN(SCIPvarGetLbLocal(consdata->bilinterms[k].var2), SCIPvarGetUbLocal(consdata->bilinterms[k].var2))),
                     +infty2infty(SCIPinfinity(scip), intervalinfty,  MAX(SCIPvarGetLbLocal(consdata->bilinterms[k].var2), SCIPvarGetUbLocal(consdata->bilinterms[k].var2))));
                  SCIPintervalMulScalar(intervalinfty, &tmp, tmp, consdata->bilinterms[k].coef);
                  SCIPintervalAdd(intervalinfty, &lincoef, lincoef, tmp);
#endif
               }

               /* deduce domain reductions for x_i */
               SCIP_CALL( propagateBoundsQuadVar(scip, cons, intervalinfty, var, consdata->quadvarterms[i].sqrcoef, lincoef, rhs2, result, nchgbds) );
               if( *result == SCIP_CUTOFF )
                  goto CLEANUP;
            }
         }
      }
   }

 CLEANUP:
   SCIPfreeBufferArrayNull(scip, &quadactcontr);

   return SCIP_OKAY;
}

/** calls domain propagation for a set of constraints */
static
SCIP_RETCODE propagateBounds(
   SCIP*                 scip,               /**< SCIP data structure */
   SCIP_CONSHDLR*        conshdlr,           /**< constraint handler */
   SCIP_CONS**           conss,              /**< constraints to process */
   int                   nconss,             /**< number of constraints */
   SCIP_RESULT*          result,             /**< pointer to store the result of the propagation calls */
   int*                  nchgbds             /**< buffer where to add the the number of changed bounds */
   )
{
   SCIP_CONSHDLRDATA* conshdlrdata;
   SCIP_RESULT propresult;
   SCIP_Bool   redundant;
   int         c;
   int         roundnr;
   SCIP_Bool   success;
   int         maxproprounds;

   assert(scip != NULL);
   assert(conshdlr != NULL);
   assert(conss != NULL || nconss == 0);
   assert(result != NULL);
   assert(nchgbds != NULL);

   assert(SCIPgetStage(scip) == SCIP_STAGE_PRESOLVING || SCIPgetStage(scip) == SCIP_STAGE_SOLVING);

   conshdlrdata = SCIPconshdlrGetData(conshdlr);
   assert(conshdlrdata != NULL);

   *result = SCIP_DIDNOTFIND;
   roundnr = 0;
   if( SCIPgetStage(scip) == SCIP_STAGE_PRESOLVING )
      maxproprounds = conshdlrdata->maxproproundspresolve;
   else
      maxproprounds = conshdlrdata->maxproprounds;

   do
   {
      success = FALSE;
      ++roundnr;

      SCIPdebugMessage("starting domain propagation round %d of %d for %d constraints\n", roundnr, maxproprounds, nconss);

      for( c = 0; c < nconss && *result != SCIP_CUTOFF; ++c )
      {
         assert(conss != NULL);
         if( !SCIPconsIsEnabled(conss[c]) )
            continue;

         SCIP_CALL( propagateBoundsCons(scip, conshdlr, conss[c], &propresult, nchgbds, &redundant) );
         if( propresult != SCIP_DIDNOTFIND && propresult != SCIP_DIDNOTRUN )
         {
            *result = propresult;
            success = TRUE;
         }
         if( redundant )
         {
            SCIPdebugMessage("deleting constraint <%s> locally\n", SCIPconsGetName(conss[c]));
            SCIP_CALL( SCIPdelConsLocal(scip, conss[c]) );
         }
      }

   }
   while( success && *result != SCIP_CUTOFF && roundnr < maxproprounds );

   return SCIP_OKAY;
}

/* checks for a linear variable that can be increase or decreased without harming feasibility */
static
void consdataFindUnlockedLinearVar(
   SCIP*                 scip,               /**< SCIP data structure */
   SCIP_CONSDATA*        consdata            /**< constraint data */
   )
{
   int i;
   int poslock;
   int neglock;

   consdata->linvar_maydecrease = -1;
   consdata->linvar_mayincrease = -1;

   /* check for a linear variable that can be increase or decreased without harming feasibility */
   for( i = 0; i < consdata->nlinvars; ++i )
   {
      /* compute locks of i'th linear variable */
      assert(consdata->lincoefs[i] != 0.0);
      if( consdata->lincoefs[i] > 0.0 )
      {
         poslock = !SCIPisInfinity(scip, -consdata->lhs) ? 1 : 0;
         neglock = !SCIPisInfinity(scip,  consdata->rhs) ? 1 : 0;
      }
      else
      {
         poslock = !SCIPisInfinity(scip,  consdata->rhs) ? 1 : 0;
         neglock = !SCIPisInfinity(scip, -consdata->lhs) ? 1 : 0;
      }

      if( SCIPvarGetNLocksDown(consdata->linvars[i]) - neglock == 0 )
      {
         /* for a*x + q(y) \in [lhs, rhs], we can decrease x without harming other constraints */
         /* if we have already one candidate, then take the one where the loss in the objective function is less */
         if( (consdata->linvar_maydecrease < 0) ||
            (SCIPvarGetObj(consdata->linvars[consdata->linvar_maydecrease]) / consdata->lincoefs[consdata->linvar_maydecrease] > SCIPvarGetObj(consdata->linvars[i]) / consdata->lincoefs[i]) )
            consdata->linvar_maydecrease = i;
      }

      if( SCIPvarGetNLocksDown(consdata->linvars[i]) - poslock == 0 )
      {
         /* for a*x + q(y) \in [lhs, rhs], we can increase x without harm */
         /* if we have already one candidate, then take the one where the loss in the objective function is less */
         if( (consdata->linvar_mayincrease < 0) ||
            (SCIPvarGetObj(consdata->linvars[consdata->linvar_mayincrease]) / consdata->lincoefs[consdata->linvar_mayincrease] > SCIPvarGetObj(consdata->linvars[i]) / consdata->lincoefs[i]) )
            consdata->linvar_mayincrease = i;
      }
   }

#ifdef SCIP_DEBUG
   if( consdata->linvar_mayincrease >= 0 )
   {
      SCIPdebugMessage("may increase <%s> to become feasible\n", SCIPvarGetName(consdata->linvars[consdata->linvar_mayincrease]));
   }
   if( consdata->linvar_maydecrease >= 0 )
   {
      SCIPdebugMessage("may decrease <%s> to become feasible\n", SCIPvarGetName(consdata->linvars[consdata->linvar_maydecrease]));
   }
#endif
}

/** Given a solution where every quadratic constraint is either feasible or can be made feasible by
 * moving a linear variable, construct the corresponding feasible solution and pass it to the trysol heuristic.
 * The method assumes that this is always possible and that not all constraints are feasible already.
 */
static
SCIP_RETCODE proposeFeasibleSolution(
   SCIP*                 scip,               /**< SCIP data structure */
   SCIP_CONSHDLR*        conshdlr,           /**< constraint handler */
   SCIP_CONS**           conss,              /**< constraints to process */
   int                   nconss,             /**< number of constraints */
   SCIP_SOL*             sol,                /**< solution to process */
   SCIP_Bool*            success             /**< buffer to store whether we succeeded to construct a solution that satisfies all provided constraints */
   )
{
   SCIP_CONSHDLRDATA* conshdlrdata;
   SCIP_CONSDATA* consdata;
   char origscaling;
   SCIP_SOL* newsol;
   SCIP_VAR* var;
   int c;
   SCIP_Real viol;
   SCIP_Real delta;
   SCIP_Real gap;

   assert(scip  != NULL);
   assert(conshdlr != NULL);
   assert(conss != NULL || nconss == 0);
   assert(success != NULL);

   *success = FALSE;

   conshdlrdata = SCIPconshdlrGetData(conshdlr);
   assert(conshdlrdata != NULL);

   if( sol != NULL )
   {
      SCIP_CALL( SCIPcreateSolCopy(scip, &newsol, sol) );
   }
   else
   {
      SCIP_CALL( SCIPcreateLPSol(scip, &newsol, NULL) );
   }
   SCIP_CALL( SCIPunlinkSol(scip, newsol) );
   SCIPdebugMessage("attempt to make solution from <%s> feasible by shifting linear variable\n",
      sol != NULL ? (SCIPsolGetHeur(sol) != NULL ? SCIPheurGetName(SCIPsolGetHeur(sol)) : "tree") : "LP");

   origscaling = conshdlrdata->scaling;
   for( c = 0; c < nconss; ++c )
   {
      consdata = SCIPconsGetData(conss[c]);  /*lint !e613*/
      assert(consdata != NULL);

      /* recompute violation of solution in case solution has changed
       * get absolution violation and sign
       * @todo avoid doing it this way
       */
      conshdlrdata->scaling = 'o';
      if( SCIPisGT(scip, consdata->lhsviol, SCIPfeastol(scip)) )
      {
         SCIP_CALL( computeViolation(scip, conshdlr, conss[c], newsol) );  /*lint !e613*/
         viol = consdata->lhs - consdata->activity;
      }
      else if( SCIPisGT(scip, consdata->rhsviol, SCIPfeastol(scip)) )
      {
         SCIP_CALL( computeViolation(scip, conshdlr, conss[c], newsol) );  /*lint !e613*/
         viol = consdata->rhs - consdata->activity;
      }
      else
         continue; /* constraint is satisfied */

      assert(viol != 0.0);
      if( consdata->linvar_mayincrease >= 0 &&
         ((viol > 0.0 && consdata->lincoefs[consdata->linvar_mayincrease] > 0.0) || (viol < 0.0 && consdata->lincoefs[consdata->linvar_mayincrease] < 0.0)) )
      {
         /* have variable where increasing makes the constraint less violated */
         var = consdata->linvars[consdata->linvar_mayincrease];
         /* compute how much we would like to increase var */
         delta = viol / consdata->lincoefs[consdata->linvar_mayincrease];
         assert(delta > 0.0);
         /* if var has an upper bound, may need to reduce delta */
         if( !SCIPisInfinity(scip, SCIPvarGetUbGlobal(var)) )
         {
            gap = SCIPvarGetUbGlobal(var) - SCIPgetSolVal(scip, newsol, var);
            delta = MIN(MAX(0.0, gap), delta);
         }
         if( SCIPisPositive(scip, delta) )
         {
            /* if variable is integral, round delta up so that it will still have an integer value */
            if( SCIPvarIsIntegral(var) )
               delta = SCIPceil(scip, delta);

            SCIP_CALL( SCIPincSolVal(scip, newsol, var, delta) );
            SCIPdebugMessage("increase <%s> by %g to %g\n", SCIPvarGetName(var), delta, SCIPgetSolVal(scip, newsol, var));

            /* adjust constraint violation, if satisfied go on to next constraint */
            viol -= consdata->lincoefs[consdata->linvar_mayincrease] * delta;
            if( SCIPisZero(scip, viol) )
               continue;
         }
      }

      assert(viol != 0.0);
      if( consdata->linvar_maydecrease >= 0 &&
         ((viol > 0.0 && consdata->lincoefs[consdata->linvar_maydecrease] < 0.0) || (viol < 0.0 && consdata->lincoefs[consdata->linvar_maydecrease] > 0.0)) )
      {
         /* have variable where decreasing makes constraint less violated */
         var = consdata->linvars[consdata->linvar_maydecrease];
         /* compute how much we would like to decrease var */
         delta = viol / consdata->lincoefs[consdata->linvar_maydecrease];
         assert(delta < 0.0);
         /* if var has a lower bound, may need to reduce delta */
         if( !SCIPisInfinity(scip, -SCIPvarGetLbGlobal(var)) )
         {
            gap = SCIPgetSolVal(scip, newsol, var) - SCIPvarGetLbGlobal(var);
            delta = MAX(MIN(0.0, gap), delta);
         }
         if( SCIPisNegative(scip, delta) )
         {
            /* if variable is integral, round delta down so that it will still have an integer value */
            if( SCIPvarIsIntegral(var) )
               delta = SCIPfloor(scip, delta);
            SCIP_CALL( SCIPincSolVal(scip, newsol, var, delta) );
            SCIPdebugMessage("increase <%s> by %g to %g\n", SCIPvarGetName(var), delta, SCIPgetSolVal(scip, newsol, var));

            /* adjust constraint violation, if satisfied go on to next constraint */
            viol -= consdata->lincoefs[consdata->linvar_maydecrease] * delta;
            if( SCIPisZero(scip, viol) )
               continue;
         }
      }

      /* still here... so probably we could not make constraint feasible due to variable bounds, thus give up */
      break;
   }
   conshdlrdata->scaling = origscaling;

   /* if we have a solution that should satisfy all quadratic constraints and has a better objective than the current upper bound,
    * then pass it to the trysol heuristic
    */
   if( c == nconss && (SCIPisInfinity(scip, SCIPgetUpperbound(scip)) || SCIPisSumLT(scip, SCIPgetSolTransObj(scip, newsol), SCIPgetUpperbound(scip))) )
   {
      SCIPdebugMessage("pass solution with objective val %g to trysol heuristic\n", SCIPgetSolTransObj(scip, newsol));

      assert(conshdlrdata->trysolheur != NULL);
      SCIP_CALL( SCIPheurPassSolTrySol(scip, conshdlrdata->trysolheur, newsol) );

      *success = TRUE;
   }

   SCIP_CALL( SCIPfreeSol(scip, &newsol) );

   return SCIP_OKAY;
}

/** tries to upgrade a nonlinear constraint into a quadratic constraint */
static
SCIP_DECL_NONLINCONSUPGD(nonlinconsUpgdQuadratic)
{
   SCIP_EXPRGRAPH* exprgraph;
   SCIP_EXPRGRAPHNODE* node;
   int i;

   assert(nupgdconss != NULL);
   assert(upgdconss != NULL);

   *nupgdconss = 0;

   node = SCIPgetExprgraphNodeNonlinear(scip, cons);

   /* no interest in linear constraints */
   if( node == NULL )
      return SCIP_OKAY;

   /* if a quadratic expression has been simplified, then all children of the node should be variables */
   if( !SCIPexprgraphAreAllNodeChildrenVars(node) )
      return SCIP_OKAY;

   switch( SCIPexprgraphGetNodeOperator(node) )
   {
   case SCIP_EXPR_VARIDX:
   case SCIP_EXPR_CONST:
   case SCIP_EXPR_PLUS:
   case SCIP_EXPR_MINUS:
   case SCIP_EXPR_SUM:
   case SCIP_EXPR_LINEAR:
      /* these should not appear as exprgraphnodes after constraint presolving */
      return SCIP_OKAY;

   case SCIP_EXPR_DIV:
   case SCIP_EXPR_SQRT:
   case SCIP_EXPR_REALPOWER:
   case SCIP_EXPR_INTPOWER:
   case SCIP_EXPR_SIGNPOWER:
   case SCIP_EXPR_EXP:
   case SCIP_EXPR_LOG:
   case SCIP_EXPR_SIN:
   case SCIP_EXPR_COS:
   case SCIP_EXPR_TAN:
      /* case SCIP_EXPR_ERF: */
      /* case SCIP_EXPR_ERFI: */
   case SCIP_EXPR_MIN:
   case SCIP_EXPR_MAX:
   case SCIP_EXPR_ABS:
   case SCIP_EXPR_SIGN:
   case SCIP_EXPR_PRODUCT:
   case SCIP_EXPR_POLYNOMIAL:
      /* these do not look like an quadratic expression (assuming the expression graph simplifier did run) */
      return SCIP_OKAY;

   case SCIP_EXPR_MUL:
   case SCIP_EXPR_SQUARE:
   case SCIP_EXPR_QUADRATIC:
      /* these mean that we have something quadratic */
      break;

   case SCIP_EXPR_PARAM:
   case SCIP_EXPR_LAST:
   default:
      SCIPwarningMessage(scip, "unexpected expression operator %d in nonlinear constraint <%s>\n", SCIPexprgraphGetNodeOperator(node), SCIPconsGetName(cons));
      return SCIP_OKAY;
   }

   /* setup a quadratic constraint */

   if( upgdconsssize < 1 )
   {
      /* request larger upgdconss array */
      *nupgdconss = -1;
      return SCIP_OKAY;
   }

   *nupgdconss = 1;
   SCIP_CALL( SCIPcreateConsQuadratic(scip, &upgdconss[0], SCIPconsGetName(cons),
         SCIPgetNLinearVarsNonlinear(scip, cons), SCIPgetLinearVarsNonlinear(scip, cons), SCIPgetLinearCoefsNonlinear(scip, cons),
         0, NULL, 0, NULL,
         SCIPgetLhsNonlinear(scip, cons), SCIPgetRhsNonlinear(scip, cons),
         SCIPconsIsInitial(cons), SCIPconsIsSeparated(cons), SCIPconsIsEnforced(cons),
         SCIPconsIsChecked(cons), SCIPconsIsPropagated(cons), SCIPconsIsLocal(cons),
         SCIPconsIsModifiable(cons), SCIPconsIsDynamic(cons), SCIPconsIsRemovable(cons)) );
   assert(!SCIPconsIsStickingAtNode(cons));

   exprgraph = SCIPgetExprgraphNonlinear(scip, SCIPconsGetHdlr(cons));

   /* add variables from expression tree as "quadratic" variables to quadratic constraint */
   for( i = 0; i < SCIPexprgraphGetNodeNChildren(node); ++i )
   {
      assert(SCIPexprgraphGetNodeChildren(node)[i] != NULL);
      SCIP_CALL( SCIPaddQuadVarQuadratic(scip, upgdconss[0], (SCIP_VAR*)SCIPexprgraphGetNodeVar(exprgraph, SCIPexprgraphGetNodeChildren(node)[i]), 0.0, 0.0) );
   }

   switch( SCIPexprgraphGetNodeOperator(node) )
   {
   case SCIP_EXPR_MUL:
      /* expression is product of two variables, so add bilinear term to constraint */
      assert(SCIPexprgraphGetNodeNChildren(node) == 2);

      SCIP_CALL( SCIPaddBilinTermQuadratic(scip, upgdconss[0],
            (SCIP_VAR*)SCIPexprgraphGetNodeVar(exprgraph, SCIPexprgraphGetNodeChildren(node)[0]),
            (SCIP_VAR*)SCIPexprgraphGetNodeVar(exprgraph, SCIPexprgraphGetNodeChildren(node)[1]),
            1.0) );

      break;

   case SCIP_EXPR_SQUARE:
      /* expression is square of a variable, so change square coefficient of quadratic variable */
      assert(SCIPexprgraphGetNodeNChildren(node) == 1);

      SCIP_CALL( SCIPaddSquareCoefQuadratic(scip, upgdconss[0],
            (SCIP_VAR*)SCIPexprgraphGetNodeVar(exprgraph, SCIPexprgraphGetNodeChildren(node)[0]),
            1.0) );

      break;

   case SCIP_EXPR_QUADRATIC:
   {
      /* expression is quadratic */
      SCIP_QUADELEM* quadelems;
      int nquadelems;
      SCIP_Real* lincoefs;

      quadelems  = SCIPexprgraphGetNodeQuadraticQuadElements(node);
      nquadelems = SCIPexprgraphGetNodeQuadraticNQuadElements(node);
      lincoefs   = SCIPexprgraphGetNodeQuadraticLinearCoefs(node);

      SCIPaddConstantQuadratic(scip, upgdconss[0], SCIPexprgraphGetNodeQuadraticConstant(node));

      if( lincoefs != NULL )
         for( i = 0; i < SCIPexprgraphGetNodeNChildren(node); ++i )
            if( lincoefs[i] != 0.0 )
            {
               /* linear term */
               SCIP_CALL( SCIPaddQuadVarLinearCoefQuadratic(scip, upgdconss[0],
                     (SCIP_VAR*)SCIPexprgraphGetNodeVar(exprgraph, SCIPexprgraphGetNodeChildren(node)[i]),
                     lincoefs[i]) );
            }

      for( i = 0; i < nquadelems; ++i )
      {
         assert(quadelems[i].idx1 < SCIPexprgraphGetNodeNChildren(node));
         assert(quadelems[i].idx2 < SCIPexprgraphGetNodeNChildren(node));

         if( quadelems[i].idx1 == quadelems[i].idx2 )
         {
            /* square term */
            SCIP_CALL( SCIPaddSquareCoefQuadratic(scip, upgdconss[0],
                  (SCIP_VAR*)SCIPexprgraphGetNodeVar(exprgraph, SCIPexprgraphGetNodeChildren(node)[quadelems[i].idx1]),
                  quadelems[i].coef) );
         }
         else
         {
            /* bilinear term */
            SCIP_CALL( SCIPaddBilinTermQuadratic(scip, upgdconss[0],
                  (SCIP_VAR*)SCIPexprgraphGetNodeVar(exprgraph, SCIPexprgraphGetNodeChildren(node)[quadelems[i].idx1]),
                  (SCIP_VAR*)SCIPexprgraphGetNodeVar(exprgraph, SCIPexprgraphGetNodeChildren(node)[quadelems[i].idx2]),
                  quadelems[i].coef) );
         }
      }

      break;
   }

   default:
      SCIPerrorMessage("you should not be here\n");
      return SCIP_ERROR;
   }  /*lint !e788 */

   return SCIP_OKAY;
}

/*
 * Callback methods of constraint handler
 */

/** copy method for constraint handler plugins (called when SCIP copies plugins) */
static
SCIP_DECL_CONSHDLRCOPY(conshdlrCopyQuadratic)
{  /*lint --e{715}*/
   assert(scip != NULL);
   assert(conshdlr != NULL);
   assert(strcmp(SCIPconshdlrGetName(conshdlr), CONSHDLR_NAME) == 0);

   /* call inclusion method of constraint handler */
   SCIP_CALL( SCIPincludeConshdlrQuadratic(scip) );

   *valid = TRUE;

   return SCIP_OKAY;
}

/** destructor of constraint handler to free constraint handler data (called when SCIP is exiting) */
static
SCIP_DECL_CONSFREE(consFreeQuadratic)
{
   SCIP_CONSHDLRDATA* conshdlrdata;
   int                i;

   assert(scip     != NULL);
   assert(conshdlr != NULL);

   conshdlrdata = SCIPconshdlrGetData(conshdlr);
   assert(conshdlrdata != NULL);

   for( i = 0; i < conshdlrdata->nquadconsupgrades; ++i )
   {
      assert(conshdlrdata->quadconsupgrades[i] != NULL);
      SCIPfreeMemory(scip, &conshdlrdata->quadconsupgrades[i]);
   }
   SCIPfreeMemoryArrayNull(scip, &conshdlrdata->quadconsupgrades);

   SCIPfreeMemory(scip, &conshdlrdata);

   return SCIP_OKAY;
}

/** initialization method of constraint handler (called after problem was transformed) */
static
SCIP_DECL_CONSINIT(consInitQuadratic)
{  /*lint --e{715} */
   SCIP_CONSHDLRDATA* conshdlrdata;
   int c;

   assert(scip != NULL);
   assert(conshdlr != NULL);

   conshdlrdata = SCIPconshdlrGetData(conshdlr);
   assert(conshdlrdata != NULL);

   conshdlrdata->subnlpheur = SCIPfindHeur(scip, "subnlp");
   conshdlrdata->trysolheur = SCIPfindHeur(scip, "trysol");

   /* catch variable events */
   for( c = 0; c < nconss; ++c )
   {
      SCIP_CALL( catchVarEvents(scip, conshdlrdata->eventhdlr, conss[c]) );
   }

   return SCIP_OKAY;
}


/** deinitialization method of constraint handler (called before transformed problem is freed) */
static
SCIP_DECL_CONSEXIT(consExitQuadratic)
{  /*lint --e{715} */
   SCIP_CONSHDLRDATA* conshdlrdata;
   int c;

   assert(scip != NULL);
   assert(conshdlr != NULL);

   conshdlrdata = SCIPconshdlrGetData(conshdlr);
   assert(conshdlrdata != NULL);

   /* drop variable events */
   for( c = 0; c < nconss; ++c )
   {
      SCIP_CALL( dropVarEvents(scip, conshdlrdata->eventhdlr, conss[c]) );
   }

   conshdlrdata->subnlpheur = NULL;
   conshdlrdata->trysolheur = NULL;

   return SCIP_OKAY;
}

/** presolving initialization method of constraint handler (called when presolving is about to begin) */
#if 0
static
SCIP_DECL_CONSINITPRE(consInitpreQuadratic)
{  /*lint --e{715}*/
   SCIP_CONSHDLRDATA* conshdlrdata;
   SCIP_CONSDATA* consdata;
   int c;

   assert(scip != NULL);
   assert(conshdlr != NULL);
   assert(conss != NULL || nconss == 0);

   conshdlrdata = SCIPconshdlrGetData(conshdlr);
   assert(conshdlrdata != NULL);

   return SCIP_OKAY;
}
#endif

/** presolving deinitialization method of constraint handler (called after presolving has been finished) */
static
SCIP_DECL_CONSEXITPRE(consExitpreQuadratic)
{  /*lint --e{715}*/
   SCIP_CONSDATA*     consdata;
   int                c;
#ifndef NDEBUG
   int                i;
#endif

   assert(scip != NULL);
   assert(conshdlr != NULL);
   assert(conss != NULL || nconss == 0);

   for( c = 0; c < nconss; ++c )
   {
      assert(conss != NULL);
      consdata = SCIPconsGetData(conss[c]);
      assert(consdata != NULL);

      if( !consdata->isremovedfixings )
      {
         SCIP_CALL( removeFixedVariables(scip, conss[c]) );
      }

      /* make sure we do not have duplicate bilinear terms, quad var terms, or linear vars */
      SCIP_CALL( mergeAndCleanBilinearTerms(scip, conss[c]) );
      SCIP_CALL( mergeAndCleanQuadVarTerms(scip, conss[c]) );
      SCIP_CALL( mergeAndCleanLinearVars(scip, conss[c]) );

      assert(consdata->isremovedfixings);
      assert(consdata->linvarsmerged);
      assert(consdata->quadvarsmerged);
      assert(consdata->bilinmerged);

#ifndef NDEBUG
      for( i = 0; i < consdata->nlinvars; ++i )
         assert(SCIPvarIsActive(consdata->linvars[i]));

      for( i = 0; i < consdata->nquadvars; ++i )
         assert(SCIPvarIsActive(consdata->quadvarterms[i].var));
#endif

      /* tell SCIP that we have something nonlinear */
      if( SCIPconsIsAdded(conss[c]) && consdata->nquadvars > 0 )
         SCIPenableNLP(scip);
   }

   return SCIP_OKAY;
}

/** solving process initialization method of constraint handler (called when branch and bound process is about to begin)
 *
 * NOTE: also called from SCIPcreateConsQuadratic(2) during solving stage
 */
static
SCIP_DECL_CONSINITSOL(consInitsolQuadratic)
{
   SCIP_CONSHDLRDATA* conshdlrdata;
   SCIP_CONSDATA*     consdata;
   int                c;
   int                i;

   assert(scip     != NULL);
   assert(conshdlr != NULL);
   assert(conss    != NULL || nconss == 0);

   conshdlrdata = SCIPconshdlrGetData(conshdlr);
   assert(conshdlrdata != NULL);

   for( c = 0; c < nconss; ++c )
   {
      assert(conss != NULL);
      consdata = SCIPconsGetData(conss[c]);
      assert(consdata != NULL);

      /* check for a linear variable that can be increase or decreased without harming feasibility */
      consdataFindUnlockedLinearVar(scip, consdata);

      /* setup lincoefsmin, lincoefsmax */
      consdata->lincoefsmin = SCIPinfinity(scip);
      consdata->lincoefsmax = 0.0;
      for( i = 0; i < consdata->nlinvars; ++i )
      {
         consdata->lincoefsmin = MIN(consdata->lincoefsmin, REALABS(consdata->lincoefs[i]));  /*lint !e666 */
         consdata->lincoefsmax = MAX(consdata->lincoefsmax, REALABS(consdata->lincoefs[i]));  /*lint !e666 */
      }

      /* add nlrow representation to NLP, if NLP had been constructed */
      if( SCIPisNLPConstructed(scip) && SCIPconsIsEnabled(conss[c]) )
      {
         if( consdata->nlrow == NULL )
         {
            SCIP_CALL( createNlRow(scip, conss[c]) );
            assert(consdata->nlrow != NULL);
         }
         SCIP_CALL( SCIPaddNlRow(scip, consdata->nlrow) );
      }

      /* setup sepaquadvars and sepabilinvar2pos */
      assert(consdata->sepaquadvars == NULL);
      assert(consdata->sepabilinvar2pos == NULL);
      if( consdata->nquadvars > 0 )
      {
         SCIP_CALL( SCIPallocBlockMemoryArray(scip, &consdata->sepaquadvars,     consdata->nquadvars) );
         SCIP_CALL( SCIPallocBlockMemoryArray(scip, &consdata->sepabilinvar2pos, consdata->nbilinterms) );

         /* make sure, quadratic variable terms are sorted */
         SCIP_CALL( consdataSortQuadVarTerms(scip, consdata) );

         for( i = 0; i < consdata->nquadvars; ++i )
            consdata->sepaquadvars[i] = consdata->quadvarterms[i].var;

         for( i = 0; i < consdata->nbilinterms; ++i )
         {
            SCIP_CALL( consdataFindQuadVarTerm(scip, consdata, consdata->bilinterms[i].var2, &consdata->sepabilinvar2pos[i]) );
         }
      }

      if( conshdlrdata->checkfactorable )
      {
         /* check if constraint function is factorable, i.e., can be written as product of two linear functions */
         SCIP_CALL( checkFactorable(scip, conss[c]) );
      }
   }

   conshdlrdata->newsoleventfilterpos = -1;
   if( nconss != 0 && conshdlrdata->linearizeheursol )
   {
      SCIP_EVENTHDLR* eventhdlr;

      eventhdlr = SCIPfindEventhdlr(scip, CONSHDLR_NAME"_newsolution");
      assert(eventhdlr != NULL);

      /* @todo Should we catch every new solution or only new *best* solutions */
      SCIP_CALL( SCIPcatchEvent(scip, SCIP_EVENTTYPE_SOLFOUND, eventhdlr, (SCIP_EVENTDATA*)conshdlr, &conshdlrdata->newsoleventfilterpos) );
   }

   if( nconss != 0 && !SCIPisIpoptAvailableIpopt() && !SCIPisInRestart(scip) )
   {
      SCIPverbMessage(scip, SCIP_VERBLEVEL_HIGH, NULL, "Quadratic constraint handler does not have LAPACK for eigenvalue computation. Will assume that matrices (with size > 2x2) are indefinite.\n");
   }

   /* reset flags and counters */
   conshdlrdata->sepanlp = FALSE;
   conshdlrdata->lastenfolpnode = NULL;
   conshdlrdata->nenfolprounds = 0;

   return SCIP_OKAY;
}

/** solving process deinitialization method of constraint handler (called before branch and bound process data is freed) */
static
SCIP_DECL_CONSEXITSOL(consExitsolQuadratic)
{  /*lint --e{715}*/
   SCIP_CONSHDLRDATA* conshdlrdata;
   SCIP_CONSDATA* consdata;
   int c;

   assert(scip != NULL);
   assert(conshdlr != NULL);
   assert(conss != NULL || nconss == 0);

   conshdlrdata = SCIPconshdlrGetData(conshdlr);
   assert(conshdlrdata != NULL);

   if( conshdlrdata->newsoleventfilterpos >= 0 )
   {
      SCIP_EVENTHDLR* eventhdlr;

      eventhdlr = SCIPfindEventhdlr(scip, CONSHDLR_NAME"_newsolution");
      assert(eventhdlr != NULL);

      SCIP_CALL( SCIPdropEvent(scip, SCIP_EVENTTYPE_SOLFOUND, eventhdlr, (SCIP_EVENTDATA*)conshdlr, conshdlrdata->newsoleventfilterpos) );
      conshdlrdata->newsoleventfilterpos = -1;
   }

   for( c = 0; c < nconss; ++c )
   {
      consdata = SCIPconsGetData(conss[c]);  /*lint !e613*/
      assert(consdata != NULL);

      /* free nonlinear row representation */
      if( consdata->nlrow != NULL )
      {
         SCIP_CALL( SCIPreleaseNlRow(scip, &consdata->nlrow) );
      }

      assert(consdata->sepaquadvars     != NULL || consdata->nquadvars == 0);
      assert(consdata->sepabilinvar2pos != NULL || consdata->nquadvars == 0);
      SCIPfreeBlockMemoryArrayNull(scip, &consdata->sepaquadvars,     consdata->nquadvars);
      SCIPfreeBlockMemoryArrayNull(scip, &consdata->sepabilinvar2pos, consdata->nbilinterms);

      SCIPfreeBlockMemoryArrayNull(scip, &consdata->factorleft,  consdata->nquadvars + 1);
      SCIPfreeBlockMemoryArrayNull(scip, &consdata->factorright, consdata->nquadvars + 1);
   }

   return SCIP_OKAY;
}

/** frees specific constraint data */
static
SCIP_DECL_CONSDELETE(consDeleteQuadratic)
{
   SCIP_CONSHDLRDATA* conshdlrdata;

   assert(scip != NULL);
   assert(conshdlr != NULL);
   assert(cons != NULL);
   assert(consdata != NULL);
   assert(SCIPconsGetData(cons) == *consdata);

   conshdlrdata = SCIPconshdlrGetData(conshdlr);
   assert(conshdlrdata != NULL);

   if( SCIPconsIsTransformed(cons) )
   {
      SCIP_CALL( dropVarEvents(scip, conshdlrdata->eventhdlr, cons) );
   }

   SCIP_CALL( consdataFree(scip, consdata) );

   assert(*consdata == NULL);

   return SCIP_OKAY;
}

/** transforms constraint data into data belonging to the transformed problem */
static
SCIP_DECL_CONSTRANS(consTransQuadratic)
{  
   SCIP_CONSDATA* sourcedata;
   SCIP_CONSDATA* targetdata;
   int            i;

   sourcedata = SCIPconsGetData(sourcecons);
   assert(sourcedata != NULL);

   SCIP_CALL( consdataCreate(scip, &targetdata,
         sourcedata->lhs, sourcedata->rhs,
         sourcedata->nlinvars, sourcedata->linvars, sourcedata->lincoefs,
         sourcedata->nquadvars, sourcedata->quadvarterms,
         sourcedata->nbilinterms, sourcedata->bilinterms,
         FALSE) );

   for( i = 0; i < targetdata->nlinvars; ++i )
   {
      SCIP_CALL( SCIPgetTransformedVar(scip, targetdata->linvars[i], &targetdata->linvars[i]) );
      SCIP_CALL( SCIPcaptureVar(scip, targetdata->linvars[i]) );
   }

   for( i = 0; i < targetdata->nquadvars; ++i )
   {
      SCIP_CALL( SCIPgetTransformedVar(scip, targetdata->quadvarterms[i].var, &targetdata->quadvarterms[i].var) );
      SCIP_CALL( SCIPcaptureVar(scip, targetdata->quadvarterms[i].var) );
   }

   for( i = 0; i < targetdata->nbilinterms; ++i )
   {
      SCIP_CALL( SCIPgetTransformedVar(scip, targetdata->bilinterms[i].var1, &targetdata->bilinterms[i].var1) );
      SCIP_CALL( SCIPgetTransformedVar(scip, targetdata->bilinterms[i].var2, &targetdata->bilinterms[i].var2) );

      if( SCIPvarCompare(targetdata->bilinterms[i].var1, targetdata->bilinterms[i].var2) > 0 )
      {
         SCIP_VAR* tmp;
         tmp = targetdata->bilinterms[i].var2;
         targetdata->bilinterms[i].var2 = targetdata->bilinterms[i].var1;
         targetdata->bilinterms[i].var1 = tmp;
      }
   }

   /* create target constraint */
   SCIP_CALL( SCIPcreateCons(scip, targetcons, SCIPconsGetName(sourcecons), conshdlr, targetdata,
         SCIPconsIsInitial(sourcecons), SCIPconsIsSeparated(sourcecons), SCIPconsIsEnforced(sourcecons),
         SCIPconsIsChecked(sourcecons), SCIPconsIsPropagated(sourcecons),  SCIPconsIsLocal(sourcecons),
         SCIPconsIsModifiable(sourcecons), SCIPconsIsDynamic(sourcecons), SCIPconsIsRemovable(sourcecons),
         SCIPconsIsStickingAtNode(sourcecons)) );

   SCIPdebugMessage("created transformed quadratic constraint ");
   SCIPdebugPrintCons(scip, *targetcons, NULL);

   return SCIP_OKAY;
}

/** LP initialization method of constraint handler (called before the initial LP relaxation at a node is solved) */
static
SCIP_DECL_CONSINITLP(consInitlpQuadratic)
{
   SCIP_CONSHDLRDATA* conshdlrdata;
   SCIP_CONSDATA*     consdata;
   SCIP_VAR*          var;
   SCIP_ROW*          row;
   SCIP_Real*         x;
   int                c;
   int                i;

   assert(scip != NULL);
   assert(conshdlr != NULL);
   assert(conss != NULL || nconss == 0);

   conshdlrdata = SCIPconshdlrGetData(conshdlr);
   assert(conshdlrdata != NULL);

   for( c = 0; c < nconss; ++c )
   {
      assert(conss[c] != NULL);  /*lint !e613 */

      SCIP_CALL( checkCurvature(scip, conss[c], conshdlrdata->checkcurvature) );  /*lint !e613 */

      consdata = SCIPconsGetData(conss[c]);  /*lint !e613 */
      assert(consdata != NULL);

      row = NULL;

      if( consdata->nquadvars == 0 )
      {
         SCIP_Bool infeasible;

         /* if we are actually linear, add the constraint as row to the LP */
         SCIP_CALL( SCIPcreateEmptyRowCons(scip, &row, SCIPconsGetHdlr(conss[c]), SCIPconsGetName(conss[c]), consdata->lhs, consdata->rhs,
               SCIPconsIsLocal(conss[c]), FALSE , TRUE) );  /*lint !e613 */
         SCIP_CALL( SCIPaddVarsToRow(scip, row, consdata->nlinvars, consdata->linvars, consdata->lincoefs) );
         SCIP_CALL( SCIPaddCut(scip, NULL, row, FALSE, &infeasible) );
         assert( ! infeasible );
         SCIP_CALL( SCIPreleaseRow (scip, &row) );
         continue;
      }

      /* alloc memory for reference point */
      SCIP_CALL( SCIPallocBufferArray(scip, &x, consdata->nquadvars) );

      /* for convex parts, add linearizations in 5 points */
      if( (consdata->isconvex && !SCIPisInfinity(scip,  consdata->rhs)) ||
         (consdata->isconcave && !SCIPisInfinity(scip, -consdata->lhs)) )
      {
         SCIP_Real lb;
         SCIP_Real ub;
         SCIP_Real lambda;
         int k;

         for( k = 0; k < 5; ++k )
         {
            lambda = 0.1 * (k+1); /* lambda = 0.1, 0.2, 0.3, 0.4, 0.5 */
            for( i = 0; i < consdata->nquadvars; ++i )
            {
               var = consdata->quadvarterms[i].var;
               lb = SCIPvarGetLbGlobal(var);
               ub = SCIPvarGetUbGlobal(var);

               if( ub > -INITLPMAXVARVAL )
                  lb = MAX(lb, -INITLPMAXVARVAL);
               if( lb <  INITLPMAXVARVAL )
                  ub = MIN(ub,  INITLPMAXVARVAL);

               /* make bounds finite */
               if( SCIPisInfinity(scip, -lb) )
                  lb = MIN(-10.0, ub - 0.1*REALABS(ub));  /*lint !e666 */
               if( SCIPisInfinity(scip,  ub) )
                  ub = MAX( 10.0, lb + 0.1*REALABS(lb));  /*lint !e666 */

               if( SCIPvarGetBestBoundType(var) == SCIP_BOUNDTYPE_LOWER )
                  x[i] = lambda * ub + (1.0 - lambda) * lb;
               else
                  x[i] = lambda * lb + (1.0 - lambda) * ub;
            }

            SCIP_CALL( generateCut(scip, conshdlr, conss[c], x, NULL, consdata->isconvex ? SCIP_SIDETYPE_RIGHT : SCIP_SIDETYPE_LEFT, &row, NULL, FALSE, -SCIPinfinity(scip)) );  /*lint !e613 */
            if( row != NULL )
            {
               SCIP_Bool infeasible;

               SCIPdebugMessage("initlp adds row <%s> for lambda = %g of conss <%s>\n", SCIProwGetName(row), lambda, SCIPconsGetName(conss[c]));  /*lint !e613 */
               SCIPdebug( SCIP_CALL( SCIPprintRow(scip, row, NULL) ) );

               SCIP_CALL( SCIPaddCut(scip, NULL, row, FALSE, &infeasible) );
               assert( ! infeasible );

               SCIP_CALL( SCIPreleaseRow (scip, &row) );
            }
         }
      }

      /* for concave parts, add underestimator w.r.t. at most 2 reference points */
      if( (!consdata->isconvex && !SCIPisInfinity(scip,  consdata->rhs)) ||
         (!consdata->isconcave && !SCIPisInfinity(scip, -consdata->lhs)) )
      {
         SCIP_Bool unbounded;
         SCIP_Bool possquare;
         SCIP_Bool negsquare;
         SCIP_Real lb;
         SCIP_Real ub;
         SCIP_Real lambda;
         int k;

         unbounded = FALSE; /* whether there are unbounded variables */
         possquare = FALSE; /* whether there is a positive square term */
         negsquare = FALSE; /* whether there is a negative square term */
         for( k = 0; k < 2; ++k )
         {
            /* set reference point to 0 projected on bounds for unbounded variables or in between lower and upper bound for bounded variables
             * in the first round, we set it closer to the best bound for one part of the variables, in the second closer to the best bound for the other part of the variables
             * additionally, we use slightly different weights for each variable
             * the reason for the latter is, that for a bilinear term with bounded variables, there are always two linear underestimators
             * if the same weight is used for both variables of a product, then rounding and luck decides which underestimator is chosen
             * of course, the possible number of cuts is something in the order of 2^nquadvars, and we choose two of them here
             */
            for( i = 0; i < consdata->nquadvars; ++i )
            {
               var = consdata->quadvarterms[i].var;
               lb = SCIPvarGetLbGlobal(var);
               ub = SCIPvarGetUbGlobal(var);

               if( SCIPisInfinity(scip, -lb) )
               {
                  if( SCIPisInfinity(scip, ub) )
                     x[i] = 0.0;
                  else
                     x[i] = MIN(0.0, ub);
                  unbounded = TRUE;
               }
               else
               {
                  if( SCIPisInfinity(scip, ub) )
                  {
                     x[i] = MAX(0.0, lb);
                     unbounded = TRUE;
                  }
                  else
                  {
                     lambda = 0.4 + 0.2 * ((i+k)%2) + 0.01 * i / (double)consdata->nquadvars;
                     x[i] = lambda * SCIPvarGetBestBoundLocal(var) + (1.0-lambda) * SCIPvarGetWorstBoundLocal(var);
                  }
               }

               possquare |= consdata->quadvarterms[i].sqrcoef > 0.0;  /*lint !e514 */
               negsquare |= consdata->quadvarterms[i].sqrcoef < 0.0;  /*lint !e514 */
            }

            if( !consdata->isconvex  && !SCIPisInfinity(scip,  consdata->rhs) )
            {
               SCIP_CALL( generateCut(scip, conshdlr, conss[c], x, NULL, SCIP_SIDETYPE_RIGHT, &row, NULL, conshdlrdata->checkcurvature, -SCIPinfinity(scip)) );  /*lint !e613 */
               if( row != NULL )
               {
                  SCIP_Bool infeasible;

                  SCIPdebugMessage("initlp adds row <%s> for rhs of conss <%s>, round %d\n", SCIProwGetName(row), SCIPconsGetName(conss[c]), k);  /*lint !e613 */
                  SCIPdebug( SCIP_CALL( SCIPprintRow(scip, row, NULL) ) );

                  SCIP_CALL( SCIPaddCut(scip, NULL, row, FALSE, &infeasible) );
                  assert( ! infeasible );

                  SCIP_CALL( SCIPreleaseRow (scip, &row) );
               }
            }
            if( !consdata->isconcave && !SCIPisInfinity(scip, -consdata->lhs) )
            {
               SCIP_CALL( generateCut(scip, conshdlr, conss[c], x, NULL, SCIP_SIDETYPE_LEFT, &row, NULL, conshdlrdata->checkcurvature, -SCIPinfinity(scip)) );  /*lint !e613 */
               if( row != NULL )
               {
                  SCIP_Bool infeasible;

                  SCIPdebugMessage("initlp adds row <%s> for lhs of conss <%s>, round %d\n", SCIProwGetName(row), SCIPconsGetName(conss[c]), k);  /*lint !e613 */
                  SCIPdebug( SCIP_CALL( SCIPprintRow(scip, row, NULL) ) );

                  SCIP_CALL( SCIPaddCut(scip, NULL, row, FALSE, &infeasible) );
                  assert( ! infeasible );

                  SCIP_CALL( SCIPreleaseRow (scip, &row) );
               }
            }

            /* if there are unbounded variables, then there is typically only at most one possible underestimator, so don't try another round
             * similar, if there are no bilinear terms and no linearizations of square terms, then the reference point does not matter, so don't do another round */
            if( unbounded ||
               (consdata->nbilinterms == 0 && (!possquare || SCIPisInfinity(scip,  consdata->rhs))) ||
               (consdata->nbilinterms == 0 && (!negsquare || SCIPisInfinity(scip, -consdata->lhs))) )
               break;
         }
      }

      SCIPfreeBufferArray(scip, &x);
   }

   return SCIP_OKAY;
}

/** separation method of constraint handler for LP solutions */
static
SCIP_DECL_CONSSEPALP(consSepalpQuadratic)
{  
   SCIP_CONSHDLRDATA* conshdlrdata;
   SCIP_CONS*         maxviolcon;

   assert(scip != NULL);
   assert(conshdlr != NULL);
   assert(conss != NULL || nconss == 0);
   assert(result != NULL);

   *result = SCIP_DIDNOTFIND;

   conshdlrdata = SCIPconshdlrGetData(conshdlr);
   assert(conshdlrdata != NULL);

   SCIP_CALL( computeViolations(scip, conshdlr, conss, nconss, NULL, &maxviolcon) );
   if( maxviolcon == NULL )
      return SCIP_OKAY;

   /* at root, check if we want to solve the NLP relaxation and use its solutions as reference point
    * if there is something convex, then linearizing in the solution of the NLP relaxation can be very useful
    */
   if( SCIPgetDepth(scip) == 0 && !conshdlrdata->sepanlp &&
      (SCIPgetNContVars(scip) >= conshdlrdata->sepanlpmincont * SCIPgetNVars(scip) || (SCIPgetLPSolstat(scip) == SCIP_LPSOLSTAT_UNBOUNDEDRAY && conshdlrdata->sepanlpmincont <= 1.0)) &&
      SCIPisNLPConstructed(scip) && SCIPgetNNlpis(scip) > 0 )
   {
      SCIP_CONSDATA*  consdata;
      SCIP_NLPSOLSTAT solstat;
      SCIP_Bool       solvednlp;
      int c;

      solstat = SCIPgetNLPSolstat(scip);
      solvednlp = FALSE;
      if( solstat == SCIP_NLPSOLSTAT_UNKNOWN )
      {
         /* NLP is not solved yet, so we might want to do this
          * but first check whether there is a violated constraint side which corresponds to a convex function
          */
         for( c = 0; c < nconss; ++c )
         {
            assert(conss[c] != NULL);  /*lint !e613 */

            consdata = SCIPconsGetData(conss[c]);  /*lint !e613 */
            assert(consdata != NULL);

            /* skip feasible constraints */
            if( !SCIPisGT(scip, consdata->lhsviol, SCIPfeastol(scip)) && !SCIPisGT(scip, consdata->rhsviol, SCIPfeastol(scip)) )
               continue;

            /* make sure curvature has been checked */
            SCIP_CALL( checkCurvature(scip, conss[c], conshdlrdata->checkcurvature) );  /*lint !e613 */

            if( (SCIPisGT(scip, consdata->rhsviol, SCIPfeastol(scip)) && consdata->isconvex) ||
               ( SCIPisGT(scip, consdata->lhsviol, SCIPfeastol(scip)) && consdata->isconcave) )
               break;
         }

         if( c < nconss )
         {
            /* try to solve NLP and update solstat */

            /* ensure linear conss are in NLP */
            if( conshdlrdata->subnlpheur != NULL )
            {
               SCIP_CALL( SCIPaddLinearConsToNlpHeurSubNlp(scip, conshdlrdata->subnlpheur, TRUE, TRUE) );
            }

            /* set LP solution as starting values, if available */
            if( SCIPgetLPSolstat(scip) == SCIP_LPSOLSTAT_OPTIMAL )
            {
               SCIP_CALL( SCIPsetNLPInitialGuessSol(scip, NULL) );
            }

            /* SCIP_CALL( SCIPsetNLPIntPar(scip, SCIP_NLPPAR_VERBLEVEL, 1) ); */
            SCIP_CALL( SCIPsolveNLP(scip) );

            solstat = SCIPgetNLPSolstat(scip);
            SCIPdebugMessage("solved NLP relax, solution status: %d\n", solstat);

            solvednlp = TRUE;
         }
      }

      conshdlrdata->sepanlp = TRUE;

      if( solstat == SCIP_NLPSOLSTAT_GLOBINFEASIBLE )
      {
         SCIPdebugMessage("NLP relaxation is globally infeasible, thus can cutoff node\n");
         *result = SCIP_CUTOFF;
         return SCIP_OKAY;
      }

      if( solstat <= SCIP_NLPSOLSTAT_FEASIBLE )
      {
         /* if we have feasible NLP solution, generate linearization cuts there */
         SCIP_Bool lpsolseparated;
         SCIP_SOL* nlpsol;

         SCIP_CALL( SCIPcreateNLPSol(scip, &nlpsol, NULL) );
         assert(nlpsol != NULL);

         /* if we solved the NLP and solution is integral, then pass it to trysol heuristic */
         if( solvednlp && conshdlrdata->trysolheur != NULL )
         {
            int nfracvars;

            nfracvars = 0;
            if( SCIPgetNBinVars(scip) > 0 || SCIPgetNIntVars(scip) > 0 )
            {
               SCIP_CALL( SCIPgetNLPFracVars(scip, NULL, NULL, NULL, &nfracvars, NULL) );
            }

            if( nfracvars == 0 )
            {
               SCIPdebugMessage("pass solution with obj. value %g to trysol\n", SCIPgetSolOrigObj(scip, nlpsol));
               SCIP_CALL( SCIPheurPassSolTrySol(scip, conshdlrdata->trysolheur, nlpsol) );
            }
         }

         SCIP_CALL( addLinearizationCuts(scip, conshdlr, conss, nconss, nlpsol, &lpsolseparated, conshdlrdata->mincutefficacysepa) );

         SCIP_CALL( SCIPfreeSol(scip, &nlpsol) );

         /* if a cut that separated the LP solution was added, then return, otherwise continue with usual separation in LP solution */
         if( lpsolseparated )
         {
            SCIPdebugMessage("linearization cuts separate LP solution\n");
            *result = SCIP_SEPARATED;

            return SCIP_OKAY;
         }
      }
   }
   /* if we do not want to try solving the NLP, or have no NLP, or have no NLP solver, or solving the NLP failed,
    * or separating with NLP solution as reference point failed, then try (again) with LP solution as reference point
    */

   SCIP_CALL( separatePoint(scip, conshdlr, conss, nconss, nusefulconss, NULL, conshdlrdata->mincutefficacysepa, FALSE, result, NULL) );

   return SCIP_OKAY;
}

/** separation method of constraint handler for arbitrary primal solutions */
static
SCIP_DECL_CONSSEPASOL(consSepasolQuadratic)
{
   SCIP_CONSHDLRDATA* conshdlrdata;
   SCIP_CONS*         maxviolcon;

   assert(scip != NULL);
   assert(conshdlr != NULL);
   assert(conss != NULL || nconss == 0);
   assert(sol != NULL);
   assert(result != NULL);

   conshdlrdata = SCIPconshdlrGetData(conshdlr);
   assert(conshdlrdata != NULL);

   *result = SCIP_DIDNOTFIND;

   SCIP_CALL( computeViolations(scip, conshdlr, conss, nconss, sol, &maxviolcon) );
   if( maxviolcon == NULL )
      return SCIP_OKAY;

   SCIP_CALL( separatePoint(scip, conshdlr, conss, nconss, nusefulconss, sol, conshdlrdata->mincutefficacysepa, FALSE, result, NULL) );

   return SCIP_OKAY;
}

/** constraint enforcing method of constraint handler for LP solutions */
static
SCIP_DECL_CONSENFOLP(consEnfolpQuadratic)
{  /*lint --e{715}*/
   SCIP_CONSHDLRDATA* conshdlrdata;
   SCIP_CONSDATA*     consdata;
   SCIP_CONS*         maxviolcon;
   SCIP_Real          maxviol;
   SCIP_RESULT        propresult;
   SCIP_RESULT        separateresult;
   int                nchgbds;
   int                nnotify;
   SCIP_Real          sepaefficacy;
   SCIP_Real          minefficacy;
   SCIP_Real          leastpossibleefficacy;

   assert(scip != NULL);
   assert(conshdlr != NULL);
   assert(conss != NULL || nconss == 0);

   conshdlrdata = SCIPconshdlrGetData(conshdlr);
   assert(conshdlrdata != NULL);

   SCIP_CALL( computeViolations(scip, conshdlr, conss, nconss, NULL, &maxviolcon) );
   if( maxviolcon == NULL )
   {
      *result = SCIP_FEASIBLE;
      return SCIP_OKAY;
   }

   *result = SCIP_INFEASIBLE;

   consdata = SCIPconsGetData(maxviolcon);
   assert(consdata != NULL);
   maxviol = consdata->lhsviol + consdata->rhsviol;
   assert(SCIPisGT(scip, maxviol, SCIPfeastol(scip)));

   SCIPdebugMessage("enfolp with max violation %g in cons <%s>\n", maxviol, SCIPconsGetName(maxviolcon));

   /* if we are above the 100'th enforcement round for this node, something is strange
    * (maybe the LP does not think that the cuts we add are violated, or we do ECP on a high-dimensional convex function)
    * in this case, check if some limit is hit or SCIP should stop for some other reason and terminate enforcement by creating a dummy node
    * (in optimized more, returning SCIP_INFEASIBLE in *result would be sufficient, but in debug mode this would give an assert in scip.c)
    * the reason to wait for 100 rounds is to avoid calls to SCIPisStopped in normal runs, which may be expensive
    * we only increment nenfolprounds until 101 to avoid an overflow
    */
   if( conshdlrdata->lastenfolpnode == SCIPgetCurrentNode(scip) )
   {
      if( conshdlrdata->nenfolprounds > 100 )
      {
         if( SCIPisStopped(scip) )
         {
            SCIP_NODE* child;

            SCIP_CALL( SCIPcreateChild(scip, &child, 1.0, SCIPnodeGetEstimate(SCIPgetCurrentNode(scip))) );
            *result = SCIP_BRANCHED;

            return SCIP_OKAY;
         }
      }

      ++conshdlrdata->nenfolprounds;

      /* cut off the current subtree, if a limit on the enforcement rounds should be applied. At this point, feasible
       * solutions might get cut off; the enfolplimit parameter should therefore only be set if SCIP is used as a
       * heuristic solver and when the returned result (infeasible, optimal, the gap) can be ignored
       */
      if( conshdlrdata->enfolplimit != -1 && conshdlrdata->nenfolprounds > conshdlrdata->enfolplimit )
      {
         SCIPverbMessage(scip, SCIP_VERBLEVEL_HIGH, NULL,
            "cut off subtree because enforcement limit was reached; this might lead to incorrect results\n");
         *result = SCIP_CUTOFF;
         return SCIP_OKAY;
      }
   }
   else
   {
      conshdlrdata->lastenfolpnode = SCIPgetCurrentNode(scip);
      conshdlrdata->nenfolprounds = 0;
   }

   /* run domain propagation */
   nchgbds = 0;
   SCIP_CALL( propagateBounds(scip, conshdlr, conss, nconss, &propresult, &nchgbds) );
   if( propresult == SCIP_CUTOFF || propresult == SCIP_REDUCEDDOM )
   {
      SCIPdebugMessage("propagation succeeded (%s)\n", propresult == SCIP_CUTOFF ? "cutoff" : "reduceddom");
      *result = propresult;
      return SCIP_OKAY;
   }

   /* we would like a cut that is efficient enough that it is not redundant in the LP (>feastol)
    * however, if the maximal violation is very small, also the best cut efficacy cannot be large
    * thus, in the latter case, we are also happy if the efficacy is at least, say, 75% of the maximal violation
    * but in any case we need an efficacy that is at least feastol
    */
   minefficacy = MIN(0.75*maxviol, conshdlrdata->mincutefficacyenfofac * SCIPfeastol(scip));  /*lint !e666 */
   minefficacy = MAX(minefficacy, SCIPfeastol(scip));  /*lint !e666 */
   SCIP_CALL( separatePoint(scip, conshdlr, conss, nconss, nusefulconss, NULL, minefficacy, TRUE, &separateresult, &sepaefficacy) );
   if( separateresult == SCIP_CUTOFF )
   {
      SCIPdebugMessage("separation found cutoff\n");
      *result = SCIP_CUTOFF;
      return SCIP_OKAY;
   }
   if( separateresult == SCIP_SEPARATED )
   {
      SCIPdebugMessage("separation succeeded (bestefficacy = %g, minefficacy = %g)\n", sepaefficacy, minefficacy);
      *result = SCIP_SEPARATED;
      return SCIP_OKAY;
   }

   /* we are not feasible, the whole node is not infeasible, and we cannot find a good cut
    * -> collect variables for branching
    */

   SCIPdebugMessage("separation failed (bestefficacy = %g < %g = minefficacy ); max viol: %g\n", sepaefficacy, minefficacy, maxviol);

   /* find branching candidates */
   SCIP_CALL( registerVariableInfeasibilities(scip, conshdlr, conss, nconss, &nnotify) );

   /* if sepastore can decrease LP feasibility tolerance, we can add cuts with efficacy in [eps, feastol] */
   leastpossibleefficacy = SCIPgetRelaxFeastolFactor(scip) > 0.0 ? SCIPepsilon(scip) : SCIPfeastol(scip);
   if( nnotify == 0 && !solinfeasible && minefficacy > leastpossibleefficacy )
   {
      /* fallback 1: we also have no branching candidates, so try to find a weak cut */
      SCIP_CALL( separatePoint(scip, conshdlr, conss, nconss, nusefulconss, NULL, leastpossibleefficacy, TRUE, &separateresult, &sepaefficacy) );
      if( separateresult == SCIP_CUTOFF )
      {
         SCIPdebugMessage("separation found cutoff\n");
         *result = SCIP_CUTOFF;
         return SCIP_OKAY;
      }
      if( separateresult == SCIP_SEPARATED )
      {
         SCIPdebugMessage("separation fallback succeeded, efficacy = %g\n", sepaefficacy);
         *result = SCIP_SEPARATED;
         return SCIP_OKAY;
      }
   }

   if( nnotify == 0 && !solinfeasible )
   {
      /* fallback 2: separation probably failed because of numerical difficulties with a convex constraint;
       *  if noone declared solution infeasible yet and we had not even found a weak cut, try to resolve by branching
       */
      SCIP_VAR* brvar = NULL;
      SCIP_CALL( registerLargeLPValueVariableForBranching(scip, conss, nconss, &brvar) );
      if( brvar == NULL )
      {
         /* fallback 3: all quadratic variables seem to be fixed -> replace by linear constraint */
         SCIP_Bool addedcons;
         SCIP_Bool reduceddom;
         SCIP_Bool infeasible;

         SCIP_CALL( replaceByLinearConstraints(scip, conss, nconss, &addedcons, &reduceddom, &infeasible) );
         /* if the linear constraints are actually feasible, then adding them and returning SCIP_CONSADDED confuses SCIP
          * when it enforces the new constraints again and nothing resolves the infeasiblity that we declare here thus,
          * we only add them if considered violated, and otherwise claim the solution is feasible (but print a
          * warning) */
         if ( infeasible )
            *result = SCIP_CUTOFF;
         else if ( addedcons )
            *result = SCIP_CONSADDED;
         else if ( reduceddom )
            *result = SCIP_REDUCEDDOM;
         else
         {
            *result = SCIP_FEASIBLE;
            SCIPwarningMessage(scip, "could not enforce feasibility by separating or branching; declaring solution with viol %g as feasible\n", maxviol);
            assert(!SCIPisInfinity(scip, maxviol));
         }
         return SCIP_OKAY;
      }
      else
      {
         SCIPdebugMessage("Could not find any usual branching variable candidate. Proposed variable <%s> with LP value %g for branching.\n",
            SCIPvarGetName(brvar), SCIPgetSolVal(scip, NULL, brvar));
         nnotify = 1;
      }
   }

   assert(*result == SCIP_INFEASIBLE && (solinfeasible || nnotify > 0));
   return SCIP_OKAY;
}


/** constraint enforcing method of constraint handler for pseudo solutions */
static
SCIP_DECL_CONSENFOPS(consEnfopsQuadratic)
{  /*lint --e{715}*/
   SCIP_CONS*         maxviolcon;
   SCIP_CONSDATA*     consdata;
   SCIP_RESULT        propresult;
   SCIP_VAR*          var;
   int                c;
   int                i;
   int                nchgbds;
   int                nnotify;

   assert(scip != NULL);
   assert(conss != NULL || nconss == 0);

   SCIP_CALL( computeViolations(scip, conshdlr, conss, nconss, NULL, &maxviolcon) );
   if( maxviolcon == NULL )
   {
      *result = SCIP_FEASIBLE;
      return SCIP_OKAY;
   }

   *result = SCIP_INFEASIBLE;

   SCIPdebugMessage("enfops with max violation in cons <%s>\n", SCIPconsGetName(maxviolcon));

   /* run domain propagation */
   nchgbds = 0;
   SCIP_CALL( propagateBounds(scip, conshdlr, conss, nconss, &propresult, &nchgbds) );
   if( propresult == SCIP_CUTOFF || propresult == SCIP_REDUCEDDOM )
   {
      *result = propresult;
      return SCIP_OKAY;
   }

   /* we are not feasible and we cannot proof that the whole node is infeasible
    * -> collect all variables in violated constraints for branching
    */
   nnotify = 0;
   for( c = 0; c < nconss; ++c )
   {
      assert(conss != NULL);
      consdata = SCIPconsGetData(conss[c]);
      assert(consdata != NULL);

      if( !SCIPisGT(scip, consdata->lhsviol, SCIPfeastol(scip)) && !SCIPisGT(scip, consdata->rhsviol, SCIPfeastol(scip)) )
         continue;

      for( i = 0; i < consdata->nlinvars; ++i )
      {
         var = consdata->linvars[i];
         if( !SCIPisRelEQ(scip, SCIPvarGetLbLocal(var), SCIPvarGetUbLocal(var)) )
         {
            SCIP_CALL( SCIPaddExternBranchCand(scip, var, MAX(consdata->lhsviol, consdata->rhsviol), SCIP_INVALID) );
            ++nnotify;
         }
      }

      for( i = 0; i < consdata->nquadvars; ++i )
      {
         var = consdata->quadvarterms[i].var;
         if( !SCIPisRelEQ(scip, SCIPvarGetLbLocal(var), SCIPvarGetUbLocal(var)) )
         {
            SCIP_CALL( SCIPaddExternBranchCand(scip, var, MAX(consdata->lhsviol, consdata->rhsviol), SCIP_INVALID) );
            ++nnotify;
         }
      }
   }

   if( nnotify == 0 )
   {
      SCIPdebugMessage("All variables in violated constraints fixed (up to epsilon). Cannot find branching candidate. Forcing solution of LP.\n");
      *result = SCIP_SOLVELP;
   }

   assert(*result == SCIP_SOLVELP || (*result == SCIP_INFEASIBLE && nnotify > 0));
   return SCIP_OKAY;
}

/** domain propagation method of constraint handler */
static
SCIP_DECL_CONSPROP(consPropQuadratic)
{
   int         nchgbds;

   assert(scip != NULL);
   assert(conshdlr != NULL);
   assert(conss != NULL || nconss == 0);
   assert(result != NULL);

   nchgbds = 0;
   SCIP_CALL( propagateBounds(scip, conshdlr, conss, nconss, result, &nchgbds) );

   return SCIP_OKAY;
}  /*lint !e715 */

/** presolving method of constraint handler */
static
SCIP_DECL_CONSPRESOL(consPresolQuadratic)
{  /*lint --e{715,788}*/
   SCIP_CONSHDLRDATA* conshdlrdata;
   SCIP_CONSDATA*     consdata;
   SCIP_RESULT        solveresult;
   SCIP_Bool          redundant;
   SCIP_Bool          havechange;
   SCIP_Bool          doreformulations;
   int                c;
   int                i;

   assert(scip     != NULL);
   assert(conshdlr != NULL);
   assert(conss    != NULL || nconss == 0);
   assert(result   != NULL);

   *result = SCIP_DIDNOTFIND;

   /* if other presolvers did not find enough changes for another presolving round,
    * then try the reformulations (replacing products with binaries, disaggregation, setting default variable bounds)
    * otherwise, we wait with these
    * @todo first do all usual presolving steps, then check SCIPisPresolveFinished(scip), and if true then do reformulations (and usual steps again)
    */
   doreformulations = (nrounds > 0 || SCIPconshdlrWasPresolvingDelayed(conshdlr)) && SCIPisPresolveFinished(scip);
   SCIPdebugMessage("presolving will %swait with reformulation\n", doreformulations ? "not " : "");

   conshdlrdata = SCIPconshdlrGetData(conshdlr);
   assert(conshdlrdata != NULL);

   for( c = 0; c < nconss; ++c )
   {
      assert(conss != NULL);
      consdata = SCIPconsGetData(conss[c]);
      assert(consdata != NULL);

      SCIPdebugMessage("process constraint <%s>\n", SCIPconsGetName(conss[c]));
      SCIPdebugPrintCons(scip, conss[c], NULL);

      if( !consdata->initialmerge )
      {
         SCIP_CALL( mergeAndCleanBilinearTerms(scip, conss[c]) );
         SCIP_CALL( mergeAndCleanQuadVarTerms(scip, conss[c]) );
         SCIP_CALL( mergeAndCleanLinearVars(scip, conss[c]) );
         consdata->initialmerge = TRUE;
      }

      havechange = FALSE;
#ifdef CHECKIMPLINBILINEAR
      if( consdata->isimpladded )
      {
         int nbilinremoved;
         SCIP_CALL( presolveApplyImplications(scip, conss[c], &nbilinremoved) );
         if( nbilinremoved > 0 )
         {
            *nchgcoefs += nbilinremoved;
            havechange = TRUE;
            *result = SCIP_SUCCESS;
         }
         assert(!consdata->isimpladded);
      }
#endif
      /* call upgrade methods if the constraint has not been presolved yet or there has been a bound tightening or possibly be a change in variable type
       * we want to do this before (multi)aggregated variables are replaced, since that may change structure, e.g., introduce bilinear terms
       */
      if( !consdata->ispresolved || !consdata->ispropagated || nnewchgvartypes > 0 )
      {
         SCIP_Bool upgraded;

         SCIP_CALL( presolveUpgrade(scip, conshdlr, conss[c], &upgraded, nupgdconss, naddconss) );
         if( upgraded )
         {
            *result = SCIP_SUCCESS;
            continue;
         }
      }

      if( !consdata->isremovedfixings )
      {
         SCIP_CALL( removeFixedVariables(scip, conss[c]) );
         assert(consdata->isremovedfixings);
         havechange = TRUE;
      }

      /* try to "solve" the constraint, e.g., reduce to a variable aggregation */
      SCIP_CALL( presolveSolve(scip, conss[c], &solveresult, &redundant, naggrvars) );
      if( solveresult == SCIP_CUTOFF )
      {
         SCIPdebugMessage("solving constraint <%s> says problem is infeasible in presolve\n", SCIPconsGetName(conss[c]));
         *result = SCIP_CUTOFF;
         return SCIP_OKAY;
      }
      if( redundant )
      {
         SCIP_CALL( dropVarEvents(scip, conshdlrdata->eventhdlr, conss[c]) );
         SCIP_CALL( SCIPdelCons(scip, conss[c]) );
         ++*ndelconss;
         *result = SCIP_SUCCESS;
         break;
      }
      if( solveresult == SCIP_SUCCESS )
      {
         *result = SCIP_SUCCESS;
         havechange = TRUE;
      }

      /* @todo divide constraint by gcd of coefficients if all are integral */

      if( doreformulations )
      {
         int naddconss_old;

         naddconss_old = *naddconss;

         SCIP_CALL( presolveTryAddAND(scip, conshdlr, conss[c], naddconss) );
         assert(*naddconss >= naddconss_old);

         if( *naddconss == naddconss_old )
         {
            /* user not so empathic about AND, or we don't have products of two binaries, so try this more general reformulation */
            SCIP_CALL( presolveTryAddLinearReform(scip, conshdlr, conss[c], naddconss) );
            assert(*naddconss >= naddconss_old);
         }

         if( conshdlrdata->disaggregate )
         {
            /* try disaggregation, if enabled */
            SCIP_CALL( presolveDisaggregate(scip, conshdlr, conss[c], naddconss) );
         }

         if( *naddconss > naddconss_old )
         {
            /* if something happened, report success and cleanup constraint */
            *result = SCIP_SUCCESS;
            havechange = TRUE;
            SCIP_CALL( mergeAndCleanBilinearTerms(scip, conss[c]) );
            SCIP_CALL( mergeAndCleanQuadVarTerms(scip, conss[c]) );
            SCIP_CALL( mergeAndCleanLinearVars(scip, conss[c]) );
         }
      }

      if( consdata->nlinvars == 0 && consdata->nquadvars == 0 )
      {
         /* all variables fixed or removed, constraint function is 0.0 now */
         SCIP_CALL( dropVarEvents(scip, conshdlrdata->eventhdlr, conss[c]) ); /* well, there shouldn't be any variables left anyway */
         if( (!SCIPisInfinity(scip, -consdata->lhs) && SCIPisFeasPositive(scip, consdata->lhs)) ||
            ( !SCIPisInfinity(scip,  consdata->rhs) && SCIPisFeasNegative(scip, consdata->rhs)) )
         { /* left hand side positive or right hand side negative */
            SCIPdebugMessage("constraint <%s> is constant and infeasible\n", SCIPconsGetName(conss[c]));
            SCIP_CALL( SCIPdelCons(scip, conss[c]) );
            ++*ndelconss;
            *result = SCIP_CUTOFF;
            return SCIP_OKAY;
         }

         /* left and right hand side are consistent */
         SCIPdebugMessage("constraint <%s> is constant and feasible, deleting\n", SCIPconsGetName(conss[c]));
         SCIP_CALL( SCIPdelCons(scip, conss[c]) );
         ++*ndelconss;
         *result = SCIP_SUCCESS;
         continue;
      }

      if( !consdata->ispropagated )
      {
         /* try domain propagation if there were bound changes or constraint has changed (in which case, processVarEvents may have set ispropagated to false) */
         SCIP_RESULT propresult;
         int roundnr;

         roundnr = 0;
         do
         {
            ++roundnr;

            SCIPdebugMessage("starting domain propagation round %d of %d\n", roundnr, conshdlrdata->maxproproundspresolve);

            SCIP_CALL( propagateBoundsCons(scip, conshdlr, conss[c], &propresult, nchgbds, &redundant) );

            if( propresult == SCIP_CUTOFF )
            {
               SCIPdebugMessage("propagation on constraint <%s> says problem is infeasible in presolve\n", SCIPconsGetName(conss[c]));
               *result = SCIP_CUTOFF;
               return SCIP_OKAY;
            }

            /* delete constraint if found redundant by bound tightening */
            if( redundant )
            {
               SCIP_CALL( dropVarEvents(scip, conshdlrdata->eventhdlr, conss[c]) );
               SCIP_CALL( SCIPdelCons(scip, conss[c]) );
               ++*ndelconss;
               *result = SCIP_SUCCESS;
               break;
            }

            if( propresult == SCIP_REDUCEDDOM )
            {
               *result = SCIP_SUCCESS;
               havechange = TRUE;
            }

         }
         while( !consdata->ispropagated && roundnr < conshdlrdata->maxproproundspresolve );

         if( redundant )
            continue;
      }

      /* check if we have a single linear continuous variable that we can make implicit integer */
      if( (nnewchgvartypes != 0 || havechange || !consdata->ispresolved)
         && (SCIPisEQ(scip, consdata->lhs, consdata->rhs) && SCIPisIntegral(scip, consdata->lhs)) )
      {
         int       ncontvar;
         SCIP_VAR* candidate;
         SCIP_Bool fail;

         fail = FALSE;
         candidate = NULL;
         ncontvar = 0;

         for( i = 0; !fail && i < consdata->nlinvars; ++i )
         {
            if( !SCIPisIntegral(scip, consdata->lincoefs[i]) )
            {
               fail = TRUE;
            }
            else if( SCIPvarGetType(consdata->linvars[i]) == SCIP_VARTYPE_CONTINUOUS )
            {
               if( ncontvar > 0 ) /* now at 2nd continuous variable */
                  fail = TRUE;
               else if( SCIPisEQ(scip, ABS(consdata->lincoefs[i]), 1.0) )
                  candidate = consdata->linvars[i];
               ++ncontvar;
            }
         }
         for( i = 0; !fail && i < consdata->nquadvars; ++i )
            fail = SCIPvarGetType(consdata->quadvarterms[i].var) == SCIP_VARTYPE_CONTINUOUS ||
               !SCIPisIntegral(scip, consdata->quadvarterms[i].lincoef) ||
               !SCIPisIntegral(scip, consdata->quadvarterms[i].sqrcoef);
         for( i = 0; !fail && i < consdata->nbilinterms; ++i )
            fail = !SCIPisIntegral(scip, consdata->bilinterms[i].coef);

         if( !fail && candidate != NULL )
         {
            SCIP_Bool infeasible;

            SCIPdebugMessage("make variable <%s> implicit integer due to constraint <%s>\n", SCIPvarGetName(candidate), SCIPconsGetName(conss[c]));

            SCIP_CALL( SCIPchgVarType(scip, candidate, SCIP_VARTYPE_IMPLINT, &infeasible) );
            if( infeasible )
            {
               SCIPdebugMessage("infeasible upgrade of variable <%s> to integral type, domain is empty\n", SCIPvarGetName(candidate));
               *result = SCIP_CUTOFF;

               return SCIP_OKAY;
            }

            ++(*nchgvartypes);
            *result = SCIP_SUCCESS;
            havechange = TRUE;
         }
      }

      /* call upgrade methods again if constraint has been changed */
      if( havechange )
      {
         SCIP_Bool upgraded;

         SCIP_CALL( presolveUpgrade(scip, conshdlr, conss[c], &upgraded, nupgdconss, naddconss) );
         if( upgraded )
         {
            *result = SCIP_SUCCESS;
            continue;
         }
      }

      consdata->ispresolved = TRUE;
   }

   /* if we did not try reformulations, ensure that presolving is called again even if there were only a few changes (< abortfac) */
   if( !doreformulations )
      *result = SCIP_DELAYED;

   return SCIP_OKAY;
}

/** variable rounding lock method of constraint handler */
static
SCIP_DECL_CONSLOCK(consLockQuadratic)
{  /*lint --e{715}*/
   SCIP_CONSDATA* consdata;
   SCIP_Bool      haslb;
   SCIP_Bool      hasub;
   int            i;

   assert(scip != NULL);
   assert(cons != NULL);

   consdata = SCIPconsGetData(cons);
   assert(consdata != NULL);

   haslb = !SCIPisInfinity(scip, -consdata->lhs);
   hasub = !SCIPisInfinity(scip, consdata->rhs);

   for( i = 0; i < consdata->nlinvars; ++i )
   {
      if( consdata->lincoefs[i] > 0 )
      {
         if( haslb )
         {
            SCIP_CALL( SCIPaddVarLocks(scip, consdata->linvars[i], nlockspos, nlocksneg) );
         }
         if( hasub )
         {
            SCIP_CALL( SCIPaddVarLocks(scip, consdata->linvars[i], nlocksneg, nlockspos) );
         }
      }
      else
      {
         if( haslb )
         {
            SCIP_CALL( SCIPaddVarLocks(scip, consdata->linvars[i], nlocksneg, nlockspos) );
         }
         if( hasub )
         {
            SCIP_CALL( SCIPaddVarLocks(scip, consdata->linvars[i], nlockspos, nlocksneg) );
         }
      }
   }

   for( i = 0; i < consdata->nquadvars; ++i )
   {
      /* @todo try to be more clever, but variable locks that depend on the bounds of other variables are not trival to maintain */
      SCIP_CALL( SCIPaddVarLocks(scip, consdata->quadvarterms[i].var, nlockspos+nlocksneg, nlockspos+nlocksneg) );
   }

   return SCIP_OKAY;
}

/** constraint display method of constraint handler */
static
SCIP_DECL_CONSPRINT(consPrintQuadratic)
{  /*lint --e{715}*/
   SCIP_CONSDATA* consdata;

   assert(scip != NULL);
   assert(cons != NULL);

   consdata = SCIPconsGetData(cons);
   assert(consdata != NULL);

   /* print left hand side for ranged rows */
   if( !SCIPisInfinity(scip, -consdata->lhs)
      && !SCIPisInfinity(scip, consdata->rhs)
      && !SCIPisEQ(scip, consdata->lhs, consdata->rhs) )
      SCIPinfoMessage(scip, file, "%.15g <= ", consdata->lhs);

   /* print coefficients and variables */
   if( consdata->nlinvars == 0 && consdata->nquadvars == 0 )
   {
      SCIPinfoMessage(scip, file, "0 ");
   }
   else
   {
      SCIP_VAR*** monomialvars;
      SCIP_Real** monomialexps;
      SCIP_Real*  monomialcoefs;
      int*        monomialnvars;
      int         nmonomials;
      int         monomialssize;
      int         j;

      monomialssize = consdata->nlinvars + 2 * consdata->nquadvars + consdata->nbilinterms;
      SCIP_CALL( SCIPallocBufferArray(scip, &monomialvars,  monomialssize) );
      SCIP_CALL( SCIPallocBufferArray(scip, &monomialexps,  monomialssize) );
      SCIP_CALL( SCIPallocBufferArray(scip, &monomialcoefs, monomialssize) );
      SCIP_CALL( SCIPallocBufferArray(scip, &monomialnvars, monomialssize) );

      nmonomials = 0;
      for( j = 0; j < consdata->nlinvars; ++j )
      {
         assert(nmonomials < monomialssize);

         SCIP_CALL( SCIPallocBufferArray(scip, &monomialvars[nmonomials], 1) );  /*lint !e866 */

         monomialvars[nmonomials][0] = consdata->linvars[j];
         monomialexps[nmonomials] = NULL;
         monomialcoefs[nmonomials] = consdata->lincoefs[j];
         monomialnvars[nmonomials] = 1;
         ++nmonomials;
      }

      for( j = 0; j < consdata->nquadvars; ++j )
      {
         if( consdata->quadvarterms[j].lincoef != 0.0 )
         {
            assert(nmonomials < monomialssize);

            SCIP_CALL( SCIPallocBufferArray(scip, &monomialvars[nmonomials], 1) );  /*lint !e866 */

            monomialvars[nmonomials][0] = consdata->quadvarterms[j].var;
            monomialexps[nmonomials] = NULL;
            monomialcoefs[nmonomials] = consdata->quadvarterms[j].lincoef;
            monomialnvars[nmonomials] = 1;
            ++nmonomials;
         }

         if( consdata->quadvarterms[j].sqrcoef != 0.0 )
         {
            assert(nmonomials < monomialssize);

            SCIP_CALL( SCIPallocBufferArray(scip, &monomialvars[nmonomials], 1) );  /*lint !e866 */
            SCIP_CALL( SCIPallocBufferArray(scip, &monomialexps[nmonomials], 1) );  /*lint !e866 */

            monomialvars[nmonomials][0] = consdata->quadvarterms[j].var;
            monomialexps[nmonomials][0] = 2.0;
            monomialcoefs[nmonomials] = consdata->quadvarterms[j].sqrcoef;
            monomialnvars[nmonomials] = 1;
            ++nmonomials;
         }
      }

      for( j = 0; j < consdata->nbilinterms; ++j )
      {
         assert(nmonomials < monomialssize);

         SCIP_CALL( SCIPallocBufferArray(scip, &monomialvars[nmonomials], 2) );  /*lint !e866 */

         monomialvars[nmonomials][0] = consdata->bilinterms[j].var1;
         monomialvars[nmonomials][1] = consdata->bilinterms[j].var2;
         monomialexps[nmonomials] = NULL;
         monomialcoefs[nmonomials] = consdata->bilinterms[j].coef;
         monomialnvars[nmonomials] = 2;
         ++nmonomials;
      }

      SCIP_CALL( SCIPwriteVarsPolynomial(scip, file, monomialvars, monomialexps, monomialcoefs, monomialnvars, nmonomials, TRUE) );

      for( j = 0; j < nmonomials; ++j )
      {
         SCIPfreeBufferArray(scip, &monomialvars[j]);
         SCIPfreeBufferArrayNull(scip, &monomialexps[j]);
      }

      SCIPfreeBufferArray(scip, &monomialvars);
      SCIPfreeBufferArray(scip, &monomialexps);
      SCIPfreeBufferArray(scip, &monomialcoefs);
      SCIPfreeBufferArray(scip, &monomialnvars);
   }

   /* print right hand side */
   if( SCIPisEQ(scip, consdata->lhs, consdata->rhs) )
   {
      SCIPinfoMessage(scip, file, " == %.15g", consdata->rhs);
   }
   else if( !SCIPisInfinity(scip, consdata->rhs) )
   {
      SCIPinfoMessage(scip, file, " <= %.15g", consdata->rhs);
   }
   else if( !SCIPisInfinity(scip, -consdata->lhs) )
   {
      SCIPinfoMessage(scip, file, " >= %.15g", consdata->lhs);
   }
   else
   {
      /* should be ignored by parser */
      SCIPinfoMessage(scip, file, " [free]");
   }

   return SCIP_OKAY;
}

/** feasibility check method of constraint handler for integral solutions */
static
SCIP_DECL_CONSCHECK(consCheckQuadratic)
{  /*lint --e{715}*/
   SCIP_CONSHDLRDATA* conshdlrdata;
   SCIP_CONSDATA*     consdata;
   SCIP_Real          maxviol;
   int                c;
   SCIP_Bool          maypropfeasible; /* whether we may be able to propose a feasible solution */

   assert(scip != NULL);
   assert(conss != NULL || nconss == 0);
   assert(result != NULL);

   conshdlrdata = SCIPconshdlrGetData(conshdlr);
   assert(conshdlrdata != NULL);

   *result = SCIP_FEASIBLE;

   maxviol = 0.0;
   maypropfeasible = conshdlrdata->linfeasshift && (conshdlrdata->trysolheur != NULL) &&
      SCIPgetStage(scip) >= SCIP_STAGE_TRANSFORMED && SCIPgetStage(scip) <= SCIP_STAGE_SOLVING;
   for( c = 0; c < nconss; ++c )
   {
      assert(conss != NULL);
      SCIP_CALL( computeViolation(scip, conshdlr, conss[c], sol) );

      consdata = SCIPconsGetData(conss[c]);
      assert(consdata != NULL);

      if( SCIPisGT(scip, consdata->lhsviol, SCIPfeastol(scip)) || SCIPisGT(scip, consdata->rhsviol, SCIPfeastol(scip)) )
      {
         *result = SCIP_INFEASIBLE;
         if( printreason )
         {
            SCIP_CALL( SCIPprintCons(scip, conss[c], NULL) );
            SCIPinfoMessage(scip, NULL, ";\n");
            if( SCIPisGT(scip, consdata->lhsviol, SCIPfeastol(scip)) )
            {
               SCIPinfoMessage(scip, NULL, "violation: left hand side is violated by %.15g (scaled: %.15g)\n", consdata->lhs - consdata->activity, consdata->lhsviol);
            }
            if( SCIPisGT(scip, consdata->rhsviol, SCIPfeastol(scip)) )
            {
               SCIPinfoMessage(scip, NULL, "violation: right hand side is violated by %.15g (scaled: %.15g)\n", consdata->activity - consdata->rhs, consdata->rhsviol);
            }
         }
         if( (conshdlrdata->subnlpheur == NULL || sol == NULL) && !maypropfeasible )
            return SCIP_OKAY;
         if( consdata->lhsviol > maxviol || consdata->rhsviol > maxviol )
            maxviol = consdata->lhsviol + consdata->rhsviol;

         /* do not try to shift linear variables if activity is at infinity (leads to setting variable to infinity in solution, which is not allowed) */
         if( maypropfeasible && SCIPisInfinity(scip, REALABS(consdata->activity)) )
            maypropfeasible = FALSE;

         if( maypropfeasible )
         {
            /* update information on linear variables that may be in- or decreased */
            if( SCIPgetStage(scip) != SCIP_STAGE_SOLVING )
               consdataFindUnlockedLinearVar(scip, consdata);

            if( SCIPisGT(scip, consdata->lhsviol, SCIPfeastol(scip)) )
            {
               /* check if there is a variable which may help to get the left hand side satisfied
                * if there is no such var, then we cannot get feasible */
               if( !(consdata->linvar_mayincrease >= 0 && consdata->lincoefs[consdata->linvar_mayincrease] > 0.0) &&
                  ! (consdata->linvar_maydecrease >= 0 && consdata->lincoefs[consdata->linvar_maydecrease] < 0.0) )
                  maypropfeasible = FALSE;
            }
            else
            {
               assert(SCIPisGT(scip, consdata->rhsviol, SCIPfeastol(scip)));
               /* check if there is a variable which may help to get the right hand side satisfied
                * if there is no such var, then we cannot get feasible */
               if( !(consdata->linvar_mayincrease >= 0 && consdata->lincoefs[consdata->linvar_mayincrease] < 0.0) &&
                  ! (consdata->linvar_maydecrease >= 0 && consdata->lincoefs[consdata->linvar_maydecrease] > 0.0) )
                  maypropfeasible = FALSE;
            }
         }
      }
   }

   if( *result == SCIP_INFEASIBLE && maypropfeasible )
   {
      SCIP_Bool success;

      SCIP_CALL( proposeFeasibleSolution(scip, conshdlr, conss, nconss, sol, &success) );

      /* do not pass solution to NLP heuristic if we made it feasible this way */
      if( success )
         return SCIP_OKAY;
   }

   if( *result == SCIP_INFEASIBLE && conshdlrdata->subnlpheur != NULL && sol != NULL )
   {
      SCIP_CALL( SCIPupdateStartpointHeurSubNlp(scip, conshdlrdata->subnlpheur, sol, maxviol) );
   }

   return SCIP_OKAY;
}

/** constraint copying method of constraint handler */
static
SCIP_DECL_CONSCOPY(consCopyQuadratic)
{
   SCIP_CONSDATA*    consdata;
   SCIP_CONSDATA*    targetconsdata;
   SCIP_VAR**        linvars;
   SCIP_QUADVARTERM* quadvarterms;
   SCIP_BILINTERM*   bilinterms;
   int               i;
   int               j;
   int               k;

   assert(scip != NULL);
   assert(cons != NULL);
   assert(sourcescip != NULL);
   assert(sourceconshdlr != NULL);
   assert(sourcecons != NULL);
   assert(varmap != NULL);
   assert(valid != NULL);

   consdata = SCIPconsGetData(sourcecons);
   assert(consdata != NULL);

   linvars = NULL;
   quadvarterms = NULL;
   bilinterms = NULL;

   *valid = TRUE;

   if( consdata->nlinvars != 0 )
   {
      SCIP_CALL( SCIPallocBufferArray(sourcescip, &linvars, consdata->nlinvars) );
      for( i = 0; i < consdata->nlinvars; ++i )
      {
         SCIP_CALL( SCIPgetVarCopy(sourcescip, scip, consdata->linvars[i], &linvars[i], varmap, consmap, global, valid) );
         assert(!(*valid) || linvars[i] != NULL);

         /* we do not copy, if a variable is missing */
         if( !(*valid) )
            goto TERMINATE;  
      }
   }

   if( consdata->nbilinterms != 0 )
   {
      SCIP_CALL( SCIPallocBufferArray(sourcescip, &bilinterms, consdata->nbilinterms) );
   }

   if( consdata->nquadvars != 0 )
   {
      SCIP_CALL( SCIPallocBufferArray(sourcescip, &quadvarterms, consdata->nquadvars) );
      for( i = 0; i < consdata->nquadvars; ++i )
      {
         SCIP_CALL( SCIPgetVarCopy(sourcescip, scip, consdata->quadvarterms[i].var, &quadvarterms[i].var, varmap, consmap, global, valid) );
         assert(!(*valid) || quadvarterms[i].var != NULL);

         /* we do not copy, if a variable is missing */
         if( !(*valid) )
            goto TERMINATE;

         quadvarterms[i].lincoef   = consdata->quadvarterms[i].lincoef;
         quadvarterms[i].sqrcoef   = consdata->quadvarterms[i].sqrcoef;
         quadvarterms[i].eventdata = NULL;
         quadvarterms[i].nadjbilin = consdata->quadvarterms[i].nadjbilin;
         quadvarterms[i].adjbilin  = consdata->quadvarterms[i].adjbilin;

         assert(consdata->nbilinterms != 0 || consdata->quadvarterms[i].nadjbilin == 0);

         for( j = 0; j < consdata->quadvarterms[i].nadjbilin; ++j )
         {
            assert(bilinterms != NULL);

            k = consdata->quadvarterms[i].adjbilin[j];
            assert(consdata->bilinterms[k].var1 != NULL);
            assert(consdata->bilinterms[k].var2 != NULL);
            if( consdata->bilinterms[k].var1 == consdata->quadvarterms[i].var )
            {
               assert(consdata->bilinterms[k].var2 != consdata->quadvarterms[i].var);
               bilinterms[k].var1 = quadvarterms[i].var;
            }
            else
            {
               assert(consdata->bilinterms[k].var2 == consdata->quadvarterms[i].var);
               bilinterms[k].var2 = quadvarterms[i].var;
            }
            bilinterms[k].coef = consdata->bilinterms[k].coef; 
         }
      }
   }

   assert(stickingatnode == FALSE);
   SCIP_CALL( SCIPcreateConsQuadratic2(scip, cons, name ? name : SCIPconsGetName(sourcecons),
         consdata->nlinvars, linvars, consdata->lincoefs,
         consdata->nquadvars, quadvarterms,
         consdata->nbilinterms, bilinterms,
         consdata->lhs, consdata->rhs,
         initial, separate, enforce, check, propagate, local, modifiable, dynamic, removable) );

   /* copy information on curvature */
   targetconsdata = SCIPconsGetData(*cons);
   targetconsdata->isconvex      = consdata->isconvex;
   targetconsdata->isconcave     = consdata->isconcave;
   targetconsdata->iscurvchecked = consdata->iscurvchecked;

 TERMINATE:
   SCIPfreeBufferArrayNull(sourcescip, &quadvarterms);
   SCIPfreeBufferArrayNull(sourcescip, &bilinterms);
   SCIPfreeBufferArrayNull(sourcescip, &linvars);

   return SCIP_OKAY;
}

/** constraint parsing method of constraint handler */
static
SCIP_DECL_CONSPARSE(consParseQuadratic)
{  /*lint --e{715}*/
   SCIP_VAR*** monomialvars;
   SCIP_Real** monomialexps;
   SCIP_Real*  monomialcoefs;
   char*       endptr;
   int*        monomialnvars;
   int         nmonomials;

   SCIP_Real lhs;
   SCIP_Real rhs;

   assert(scip != NULL);
   assert(success != NULL);
   assert(str != NULL);
   assert(name != NULL);
   assert(cons != NULL);

   /* set left and right hand side to their default values */
   lhs = -SCIPinfinity(scip);
   rhs =  SCIPinfinity(scip);

   (*success) = FALSE;

   /* return of string empty */
   if( !*str )
      return SCIP_OKAY;

   /* ignore whitespace */
   while( isspace((unsigned char)*str) )
      ++str;

   /* check for left hand side */
   if( isdigit((unsigned char)str[0]) || ((str[0] == '-' || str[0] == '+') && isdigit((unsigned char)str[1])) )
   {
      /* there is a number coming, maybe it is a left-hand-side */
      if( !SCIPstrToRealValue(str, &lhs, &endptr) )
      {
         SCIPerrorMessage("error parsing number from <%s>\n", str);
         return SCIP_OKAY;
      }

      /* ignore whitespace */
      while( isspace((unsigned char)*endptr) )
         ++endptr;

      if( endptr[0] != '<' || endptr[1] != '=' )
      {
         /* no '<=' coming, so it was the first coefficient, but not a left-hand-side */
         lhs = -SCIPinfinity(scip);
      }
      else
      {
         /* it was indeed a left-hand-side, so continue parsing after it */
         str = endptr + 2;

         /* ignore whitespace */
         while( isspace((unsigned char)*str) )
            ++str;
      }
   }

   SCIP_CALL( SCIPparseVarsPolynomial(scip, str, &monomialvars, &monomialexps, &monomialcoefs, &monomialnvars, &nmonomials, &endptr, success) );

   if( *success )
   {
      /* check for right hand side */
      str = endptr;

      /* ignore whitespace */
      while( isspace((unsigned char)*str) )
         ++str;

      if( *str && str[0] == '<' && str[1] == '=' )
      {
         /* we seem to get a right-hand-side */
         str += 2;

         if( !SCIPstrToRealValue(str, &rhs, &endptr) )
         {
            SCIPerrorMessage("error parsing right-hand-side from %s\n", str);
            *success = FALSE;
         }
      }
      else if( *str && str[0] == '>' && str[1] == '=' )
      {
         /* we seem to get a left-hand-side */
         str += 2;

         /* we should not have a left-hand-side already */
         assert(SCIPisInfinity(scip, -lhs));

         if( !SCIPstrToRealValue(str, &lhs, &endptr) )
         {
            SCIPerrorMessage("error parsing left-hand-side from %s\n", str);
            *success = FALSE;
         }
      }
      else if( *str && str[0] == '=' && str[1] == '=' )
      {
         /* we seem to get a left- and right-hand-side */
         str += 2;

         /* we should not have a left-hand-side already */
         assert(SCIPisInfinity(scip, -lhs));

         if( !SCIPstrToRealValue(str, &lhs, &endptr) )
         {
            SCIPerrorMessage("error parsing left-hand-side from %s\n", str);
            *success = FALSE;
         }
         else
         {
            rhs = lhs;
         }
      }
   }

   if( *success )
   {
      int i;

      /* setup constraint */
      assert(stickingatnode == FALSE);
      SCIP_CALL( SCIPcreateConsQuadratic(scip, cons, name, 0, NULL, NULL,
            0, NULL, NULL, NULL, lhs, rhs,
            initial, separate, enforce, check, propagate, local, modifiable, dynamic, removable) );

      for( i = 0; i < nmonomials; ++i )
      {
         if( monomialnvars[i] == 0 )
         {
            /* constant monomial */
            SCIPaddConstantQuadratic(scip, *cons, monomialcoefs[i]);
         }
         else if( monomialnvars[i] == 1 && monomialexps[i][0] == 1.0 )
         {
            /* linear monomial */
            SCIP_CALL( SCIPaddLinearVarQuadratic(scip, *cons, monomialvars[i][0], monomialcoefs[i]) );
         }
         else if( monomialnvars[i] == 1 && monomialexps[i][0] == 2.0 )
         {
            /* square monomial */
            SCIP_CALL( SCIPaddQuadVarQuadratic(scip, *cons, monomialvars[i][0], 0.0, monomialcoefs[i]) );
         }
         else if( monomialnvars[i] == 2 && monomialexps[i][0] == 1.0 && monomialexps[i][1] == 1.0 )
         {
            /* bilinear term */
            SCIP_VAR* var1;
            SCIP_VAR* var2;
            int pos;

            var1 = monomialvars[i][0];
            var2 = monomialvars[i][1];
            if( var1 == var2 )
            {
               /* actually a square term */
               SCIP_CALL( SCIPaddQuadVarQuadratic(scip, *cons, var1, 0.0, monomialcoefs[i]) );
            }
            else
            {
               SCIP_CALL( SCIPfindQuadVarTermQuadratic(scip, *cons, var1, &pos) );
               if( pos == -1 )
               {
                  SCIP_CALL( SCIPaddQuadVarQuadratic(scip, *cons, var1, 0.0, 0.0) );
               }

               SCIP_CALL( SCIPfindQuadVarTermQuadratic(scip, *cons, var2, &pos) );
               if( pos == -1 )
               {
                  SCIP_CALL( SCIPaddQuadVarQuadratic(scip, *cons, var2, 0.0, 0.0) );
               }
            }

            SCIP_CALL( SCIPaddBilinTermQuadratic(scip, *cons, var1, var2, monomialcoefs[i]) );
         }
         else
         {
            SCIPerrorMessage("polynomial in quadratic constraint does not have degree at most 2\n");
            *success = FALSE;
            SCIP_CALL( SCIPreleaseCons(scip, cons) );
            break;
         }
      }
   }

   SCIPfreeParseVarsPolynomialData(scip, &monomialvars, &monomialexps, &monomialcoefs, &monomialnvars, nmonomials);

   return SCIP_OKAY;
}

/** constraint method of constraint handler which returns the variables (if possible) */
static
SCIP_DECL_CONSGETVARS(consGetVarsQuadratic)
{  /*lint --e{715}*/
   SCIP_CONSDATA* consdata;

   assert(cons != NULL);
   assert(success != NULL);

   consdata = SCIPconsGetData(cons);
   assert(consdata != NULL);

   if( varssize < consdata->nlinvars + consdata->nquadvars )
      (*success) = FALSE;
   else
   {
      int i;

      assert(vars != NULL);

      BMScopyMemoryArray(vars, consdata->linvars, consdata->nlinvars);

      for( i = 0; i < consdata->nquadvars; ++i )
         vars[consdata->nlinvars+i] = consdata->quadvarterms[i].var;

      (*success) = TRUE;
   }

   return SCIP_OKAY;
}

/** constraint method of constraint handler which returns the number of variables (if possible) */
static
SCIP_DECL_CONSGETNVARS(consGetNVarsQuadratic)
{  /*lint --e{715}*/
   SCIP_CONSDATA* consdata;

   assert(cons != NULL);
   assert(success != NULL);

   consdata = SCIPconsGetData(cons);
   assert(consdata != NULL);

   (*nvars) = consdata->nlinvars + consdata->nquadvars;
   (*success) = TRUE;

   return SCIP_OKAY;
}


/*
 * constraint specific interface methods
 */

/** creates the handler for quadratic constraints and includes it in SCIP */
SCIP_RETCODE SCIPincludeConshdlrQuadratic(
   SCIP*                 scip                /**< SCIP data structure */
   )
{
   SCIP_CONSHDLRDATA* conshdlrdata;
   SCIP_CONSHDLR* conshdlr;

   /* create quadratic constraint handler data */
   SCIP_CALL( SCIPallocMemory(scip, &conshdlrdata) );
   BMSclearMemory(conshdlrdata);

   /* include constraint handler */
   SCIP_CALL( SCIPincludeConshdlrBasic(scip, &conshdlr, CONSHDLR_NAME, CONSHDLR_DESC,
         CONSHDLR_ENFOPRIORITY, CONSHDLR_CHECKPRIORITY, CONSHDLR_EAGERFREQ, CONSHDLR_NEEDSCONS,
         consEnfolpQuadratic, consEnfopsQuadratic, consCheckQuadratic, consLockQuadratic,
         conshdlrdata) );
   assert(conshdlr != NULL);


   /* set non-fundamental callbacks via specific setter functions */
   SCIP_CALL( SCIPsetConshdlrCopy(scip, conshdlr, conshdlrCopyQuadratic, consCopyQuadratic) );
   SCIP_CALL( SCIPsetConshdlrDelete(scip, conshdlr, consDeleteQuadratic) );
   SCIP_CALL( SCIPsetConshdlrExit(scip, conshdlr, consExitQuadratic) );
   SCIP_CALL( SCIPsetConshdlrExitpre(scip, conshdlr, consExitpreQuadratic) );
   SCIP_CALL( SCIPsetConshdlrExitsol(scip, conshdlr, consExitsolQuadratic) );
   SCIP_CALL( SCIPsetConshdlrFree(scip, conshdlr, consFreeQuadratic) );
   SCIP_CALL( SCIPsetConshdlrGetVars(scip, conshdlr, consGetVarsQuadratic) );
   SCIP_CALL( SCIPsetConshdlrGetNVars(scip, conshdlr, consGetNVarsQuadratic) );
   SCIP_CALL( SCIPsetConshdlrInit(scip, conshdlr, consInitQuadratic) );
   SCIP_CALL( SCIPsetConshdlrInitsol(scip, conshdlr, consInitsolQuadratic) );
   SCIP_CALL( SCIPsetConshdlrInitlp(scip, conshdlr, consInitlpQuadratic) );
   SCIP_CALL( SCIPsetConshdlrParse(scip, conshdlr, consParseQuadratic) );
   SCIP_CALL( SCIPsetConshdlrPresol(scip, conshdlr, consPresolQuadratic, CONSHDLR_MAXPREROUNDS, CONSHDLR_DELAYPRESOL) );
   SCIP_CALL( SCIPsetConshdlrPrint(scip, conshdlr, consPrintQuadratic) );
   SCIP_CALL( SCIPsetConshdlrProp(scip, conshdlr, consPropQuadratic, CONSHDLR_PROPFREQ, CONSHDLR_DELAYPROP,
         CONSHDLR_PROP_TIMING) );
   SCIP_CALL( SCIPsetConshdlrSepa(scip, conshdlr, consSepalpQuadratic, consSepasolQuadratic, CONSHDLR_SEPAFREQ,
         CONSHDLR_SEPAPRIORITY, CONSHDLR_DELAYSEPA) );
   SCIP_CALL( SCIPsetConshdlrTrans(scip, conshdlr, consTransQuadratic) );

   /* add quadratic constraint handler parameters */
   SCIP_CALL( SCIPaddIntParam(scip, "constraints/"CONSHDLR_NAME"/replacebinaryprod",
         "max. length of linear term which when multiplied with a binary variables is replaced by an auxiliary variable and a linear reformulation (0 to turn off)",
         &conshdlrdata->replacebinaryprodlength, FALSE, INT_MAX, 0, INT_MAX, NULL, NULL) );

   SCIP_CALL( SCIPaddIntParam(scip, "constraints/"CONSHDLR_NAME"/empathy4and",
         "empathy level for using the AND constraint handler: 0 always avoid using AND; 1 use AND sometimes; 2 use AND as often as possible",
         &conshdlrdata->empathy4and, FALSE, 0, 0, 2, NULL, NULL) );

   SCIP_CALL( SCIPaddBoolParam(scip, "constraints/"CONSHDLR_NAME"/binreforminitial",
         "whether to make non-varbound linear constraints added due to replacing products with binary variables initial",
         &conshdlrdata->binreforminitial, TRUE, FALSE, NULL, NULL) );

   SCIP_CALL( SCIPaddRealParam(scip, "constraints/"CONSHDLR_NAME"/binreformmaxcoef",
         "limit (as factor on 1/feastol) on coefficients and coef. range in linear constraints created when replacing products with binary variables",
         &conshdlrdata->binreformmaxcoef, TRUE, 1e-4, 0.0, SCIPinfinity(scip), NULL, NULL) );

   SCIP_CALL( SCIPaddRealParam(scip, "constraints/"CONSHDLR_NAME"/minefficacysepa",
         "minimal efficacy for a cut to be added to the LP during separation; overwrites separating/efficacy",
         &conshdlrdata->mincutefficacysepa, TRUE, 0.0001, 0.0, SCIPinfinity(scip), NULL, NULL) );

   SCIP_CALL( SCIPaddRealParam(scip, "constraints/"CONSHDLR_NAME"/minefficacyenfofac",
         "minimal target efficacy of a cut in order to add it to relaxation during enforcement as a factor of the feasibility tolerance (may be ignored)",
         &conshdlrdata->mincutefficacyenfofac, TRUE, 2.0, 1.0, SCIPinfinity(scip), NULL, NULL) );

   SCIP_CALL( SCIPaddCharParam(scip, "constraints/"CONSHDLR_NAME"/scaling",
         "whether scaling of infeasibility is 'o'ff, by sup-norm of function 'g'radient, or by left/right hand 's'ide",
         &conshdlrdata->scaling, TRUE, 'o', "ogs", NULL, NULL) );

   SCIP_CALL( SCIPaddRealParam(scip, "constraints/"CONSHDLR_NAME"/cutmaxrange",
         "maximal coef range of a cut (maximal coefficient divided by minimal coefficient) in order to be added to LP relaxation",
         &conshdlrdata->cutmaxrange, TRUE, 1e+7, 0.0, SCIPinfinity(scip), NULL, NULL) );

   SCIP_CALL( SCIPaddBoolParam(scip, "constraints/"CONSHDLR_NAME"/linearizeheursol",
         "whether linearizations of convex quadratic constraints should be added to cutpool in a solution found by some heuristic",
         &conshdlrdata->linearizeheursol, TRUE, TRUE, NULL, NULL) );

   SCIP_CALL( SCIPaddBoolParam(scip, "constraints/"CONSHDLR_NAME"/checkcurvature",
         "whether multivariate quadratic functions should be checked for convexity/concavity",
         &conshdlrdata->checkcurvature, FALSE, TRUE, NULL, NULL) );

   SCIP_CALL( SCIPaddBoolParam(scip, "constraints/"CONSHDLR_NAME"/checkfactorable",
         "whether constraint functions should be checked to be factorable",
         &conshdlrdata->checkfactorable, TRUE, TRUE, NULL, NULL) );

   SCIP_CALL( SCIPaddBoolParam(scip, "constraints/"CONSHDLR_NAME"/linfeasshift",
         "whether to try to make solutions in check function feasible by shifting a linear variable (esp. useful if constraint was actually objective function)",
         &conshdlrdata->linfeasshift, TRUE, TRUE, NULL, NULL) );

   SCIP_CALL( SCIPaddBoolParam(scip, "constraints/"CONSHDLR_NAME"/disaggregate",
         "whether to disaggregate quadratic parts that decompose into a sum of non-overlapping quadratic terms",
         &conshdlrdata->disaggregate, TRUE, FALSE, NULL, NULL) );

   SCIP_CALL( SCIPaddIntParam(scip, "constraints/"CONSHDLR_NAME"/maxproprounds",
         "limit on number of propagation rounds for a single constraint within one round of SCIP propagation during solve",
         &conshdlrdata->maxproprounds, TRUE, 1, 0, INT_MAX, NULL, NULL) );

   SCIP_CALL( SCIPaddIntParam(scip, "constraints/"CONSHDLR_NAME"/maxproproundspresolve",
         "limit on number of propagation rounds for a single constraint within one round of SCIP presolve",
         &conshdlrdata->maxproproundspresolve, TRUE, 10, 0, INT_MAX, NULL, NULL) );

   SCIP_CALL( SCIPaddIntParam(scip, "constraints/"CONSHDLR_NAME"/enfolplimit",
         "maximum number of enforcement rounds before declaring the LP relaxation infeasible (-1: no limit); WARNING: changing this parameter might lead to incorrect results!",
         &conshdlrdata->enfolplimit, TRUE, -1, -1, INT_MAX, NULL, NULL) );

   SCIP_CALL( SCIPaddRealParam(scip, "constraints/"CONSHDLR_NAME"/sepanlpmincont",
         "minimal required fraction of continuous variables in problem to use solution of NLP relaxation in root for separation",
         &conshdlrdata->sepanlpmincont, FALSE, 1.0, 0.0, 2.0, NULL, NULL) );

   SCIP_CALL( SCIPaddBoolParam(scip, "constraints/"CONSHDLR_NAME"/enfocutsremovable",
         "are cuts added during enforcement removable from the LP in the same node?",
         &conshdlrdata->enfocutsremovable, TRUE, FALSE, NULL, NULL) );

   conshdlrdata->eventhdlr = NULL;
   SCIP_CALL( SCIPincludeEventhdlrBasic(scip, &(conshdlrdata->eventhdlr),CONSHDLR_NAME"_boundchange", "signals a bound change to a quadratic constraint",
         processVarEvent, NULL) );
   assert(conshdlrdata->eventhdlr != NULL);

   SCIP_CALL( SCIPincludeEventhdlrBasic(scip, NULL, CONSHDLR_NAME"_newsolution", "handles the event that a new primal solution has been found",
         processNewSolutionEvent, NULL) );

   /* include the quadratic constraint upgrade in the nonlinear constraint handler */
   SCIP_CALL( SCIPincludeNonlinconsUpgrade(scip, nonlinconsUpgdQuadratic, NULL, NONLINCONSUPGD_PRIORITY, TRUE, CONSHDLR_NAME) );

   return SCIP_OKAY;
}

/** includes a quadratic constraint update method into the quadratic constraint handler */
SCIP_RETCODE SCIPincludeQuadconsUpgrade(
   SCIP*                 scip,               /**< SCIP data structure */
   SCIP_DECL_QUADCONSUPGD((*quadconsupgd)),  /**< method to call for upgrading quadratic constraint */
   int                   priority,           /**< priority of upgrading method */
   SCIP_Bool             active,             /**< should the upgrading method be active by default? */
   const char*           conshdlrname        /**< name of the constraint handler */
   )
{
   SCIP_CONSHDLR*        conshdlr;
   SCIP_CONSHDLRDATA*    conshdlrdata;
   SCIP_QUADCONSUPGRADE* quadconsupgrade;
   char                  paramname[SCIP_MAXSTRLEN];
   char                  paramdesc[SCIP_MAXSTRLEN];
   int                   i;

   assert(quadconsupgd != NULL);
   assert(conshdlrname != NULL );

   /* find the quadratic constraint handler */
   conshdlr = SCIPfindConshdlr(scip, CONSHDLR_NAME);
   if( conshdlr == NULL )
   {
      SCIPerrorMessage("quadratic constraint handler not found\n");
      return SCIP_PLUGINNOTFOUND;
   }

   conshdlrdata = SCIPconshdlrGetData(conshdlr);
   assert(conshdlrdata != NULL);

   if( !conshdlrdataHasUpgrade(scip, conshdlrdata, quadconsupgd, conshdlrname) )
   {
      /* create a quadratic constraint upgrade data object */
      SCIP_CALL( SCIPallocMemory(scip, &quadconsupgrade) );
      quadconsupgrade->quadconsupgd = quadconsupgd;
      quadconsupgrade->priority     = priority;
      quadconsupgrade->active       = active;

      /* insert quadratic constraint upgrade method into constraint handler data */
      assert(conshdlrdata->nquadconsupgrades <= conshdlrdata->quadconsupgradessize);
      if( conshdlrdata->nquadconsupgrades+1 > conshdlrdata->quadconsupgradessize )
      {
         int newsize;

         newsize = SCIPcalcMemGrowSize(scip, conshdlrdata->nquadconsupgrades+1);
         SCIP_CALL( SCIPreallocMemoryArray(scip, &conshdlrdata->quadconsupgrades, newsize) );
         conshdlrdata->quadconsupgradessize = newsize;
      }
      assert(conshdlrdata->nquadconsupgrades+1 <= conshdlrdata->quadconsupgradessize);

      for( i = conshdlrdata->nquadconsupgrades; i > 0 && conshdlrdata->quadconsupgrades[i-1]->priority < quadconsupgrade->priority; --i )
         conshdlrdata->quadconsupgrades[i] = conshdlrdata->quadconsupgrades[i-1];
      assert(0 <= i && i <= conshdlrdata->nquadconsupgrades);
      conshdlrdata->quadconsupgrades[i] = quadconsupgrade;
      conshdlrdata->nquadconsupgrades++;

      /* adds parameter to turn on and off the upgrading step */
      (void) SCIPsnprintf(paramname, SCIP_MAXSTRLEN, "constraints/"CONSHDLR_NAME"/upgrade/%s", conshdlrname);
      (void) SCIPsnprintf(paramdesc, SCIP_MAXSTRLEN, "enable quadratic upgrading for constraint handler <%s>", conshdlrname);
      SCIP_CALL( SCIPaddBoolParam(scip,
            paramname, paramdesc,
            &quadconsupgrade->active, FALSE, active, NULL, NULL) );
   }

   return SCIP_OKAY;
}

/** Creates and captures a quadratic constraint.
 * 
 *  The constraint should be given in the form
 *  \f[
 *  \ell \leq \sum_{i=1}^n b_i x_i + \sum_{j=1}^m a_j y_jz_j \leq u,
 *  \f]
 *  where \f$x_i = y_j = z_k\f$ is possible.
 *
 *  @note the constraint gets captured, hence at one point you have to release it using the method SCIPreleaseCons()
 */
SCIP_RETCODE SCIPcreateConsQuadratic(
   SCIP*                 scip,               /**< SCIP data structure */
   SCIP_CONS**           cons,               /**< pointer to hold the created constraint */
   const char*           name,               /**< name of constraint */
   int                   nlinvars,           /**< number of linear terms (n) */
   SCIP_VAR**            linvars,            /**< array with variables in linear part (x_i) */
   SCIP_Real*            lincoefs,           /**< array with coefficients of variables in linear part (b_i) */
   int                   nquadterms,         /**< number of quadratic terms (m) */
   SCIP_VAR**            quadvars1,          /**< array with first variables in quadratic terms (y_j) */
   SCIP_VAR**            quadvars2,          /**< array with second variables in quadratic terms (z_j) */
   SCIP_Real*            quadcoefs,          /**< array with coefficients of quadratic terms (a_j) */
   SCIP_Real             lhs,                /**< left hand side of quadratic equation (ell) */
   SCIP_Real             rhs,                /**< right hand side of quadratic equation (u) */
   SCIP_Bool             initial,            /**< should the LP relaxation of constraint be in the initial LP?
                                              *   Usually set to TRUE. Set to FALSE for 'lazy constraints'. */
   SCIP_Bool             separate,           /**< should the constraint be separated during LP processing?
                                              *   Usually set to TRUE. */
   SCIP_Bool             enforce,            /**< should the constraint be enforced during node processing?
                                              *   TRUE for model constraints, FALSE for additional, redundant constraints. */
   SCIP_Bool             check,              /**< should the constraint be checked for feasibility?
                                              *   TRUE for model constraints, FALSE for additional, redundant constraints. */
   SCIP_Bool             propagate,          /**< should the constraint be propagated during node processing?
                                              *   Usually set to TRUE. */
   SCIP_Bool             local,              /**< is constraint only valid locally?
                                              *   Usually set to FALSE. Has to be set to TRUE, e.g., for branching constraints. */
   SCIP_Bool             modifiable,         /**< is constraint modifiable (subject to column generation)?
                                              *   Usually set to FALSE. In column generation applications, set to TRUE if pricing
                                              *   adds coefficients to this constraint. */
   SCIP_Bool             dynamic,            /**< is constraint subject to aging?
                                              *   Usually set to FALSE. Set to TRUE for own cuts which
                                              *   are separated as constraints. */
   SCIP_Bool             removable           /**< should the relaxation be removed from the LP due to aging or cleanup?
                                              *   Usually set to FALSE. Set to TRUE for 'lazy constraints' and 'user cuts'. */
   )
{
   SCIP_CONSHDLR* conshdlr;
   SCIP_CONSDATA* consdata;
   SCIP_HASHMAP*  quadvaridxs;
   SCIP_Real      sqrcoef;
   int i;
   int var1pos;
   int var2pos;

   int nbilinterms;

   assert(modifiable == FALSE); /* we do not support column generation */

   /* find the quadratic constraint handler */
   conshdlr = SCIPfindConshdlr(scip, CONSHDLR_NAME);
   if( conshdlr == NULL )
   {
      SCIPerrorMessage("quadratic constraint handler not found\n");
      return SCIP_PLUGINNOTFOUND;
   }

   /* create constraint data and constraint */
   SCIP_CALL( consdataCreateEmpty(scip, &consdata) );

   consdata->lhs = lhs;
   consdata->rhs = rhs;

   SCIP_CALL( SCIPcreateCons(scip, cons, name, conshdlr, consdata, initial, separate, enforce, check, propagate,
         local, modifiable, dynamic, removable, FALSE) );

   /* add quadratic variables and remember their indices */
   SCIP_CALL( SCIPhashmapCreate(&quadvaridxs, SCIPblkmem(scip), SCIPcalcHashtableSize(5 * nquadterms)) );
   nbilinterms = 0;
   for( i = 0; i < nquadterms; ++i )
   {
      if( SCIPisZero(scip, quadcoefs[i]) )
         continue;

      /* if it is actually a square term, remember it's coefficient */
      if( quadvars1[i] == quadvars2[i] )
         sqrcoef = quadcoefs[i];
      else
         sqrcoef = 0.0;

      /* add quadvars1[i], if not in there already */
      if( !SCIPhashmapExists(quadvaridxs, quadvars1[i]) )
      {
         SCIP_CALL( addQuadVarTerm(scip, *cons, quadvars1[i], 0.0, sqrcoef, FALSE) );
         assert(consdata->nquadvars >= 0);
         assert(consdata->quadvarterms[consdata->nquadvars-1].var == quadvars1[i]);

         SCIP_CALL( SCIPhashmapInsert(quadvaridxs, quadvars1[i], (void*)(size_t)(consdata->nquadvars-1)) );
      }
      else if( !SCIPisZero(scip, sqrcoef) )
      {
         /* if it's there already, but we got a square coefficient, add it to the previous one */ 
         var1pos = (int) (size_t) SCIPhashmapGetImage(quadvaridxs, quadvars1[i]);
         assert(consdata->quadvarterms[var1pos].var == quadvars1[i]);
         consdata->quadvarterms[var1pos].sqrcoef += sqrcoef;
      }

      if( quadvars1[i] == quadvars2[i] )
         continue;

      /* add quadvars2[i], if not in there already */
      if( !SCIPhashmapExists(quadvaridxs, quadvars2[i]) )
      {
         assert(sqrcoef == 0.0);
         SCIP_CALL( addQuadVarTerm(scip, *cons, quadvars2[i], 0.0, 0.0, FALSE) );
         assert(consdata->nquadvars >= 0);
         assert(consdata->quadvarterms[consdata->nquadvars-1].var == quadvars2[i]);

         SCIP_CALL( SCIPhashmapInsert(quadvaridxs, quadvars2[i], (void*)(size_t)(consdata->nquadvars-1)) );
      }

      ++nbilinterms;
   }

   /* add bilinear terms, if we saw any */
   if( nbilinterms > 0 )
   {
      SCIP_CALL( consdataEnsureBilinSize(scip, consdata, nbilinterms) );
      for( i = 0; i < nquadterms; ++i )
      {
         if( SCIPisZero(scip, quadcoefs[i]) )
            continue;

         /* square terms have been taken care of already */
         if( quadvars1[i] == quadvars2[i] )
            continue;

         assert(SCIPhashmapExists(quadvaridxs, quadvars1[i]));
         assert(SCIPhashmapExists(quadvaridxs, quadvars2[i]));

         var1pos = (int) (size_t) SCIPhashmapGetImage(quadvaridxs, quadvars1[i]);
         var2pos = (int) (size_t) SCIPhashmapGetImage(quadvaridxs, quadvars2[i]);

         SCIP_CALL( addBilinearTerm(scip, *cons, var1pos, var2pos, quadcoefs[i]) );
      }
   }

   /* add linear variables */
   SCIP_CALL( consdataEnsureLinearVarsSize(scip, consdata, nlinvars) );
   for( i = 0; i < nlinvars; ++i )
   {
      if( SCIPisZero(scip, lincoefs[i]) )
         continue;

      /* if it's a linear coefficient for a quadratic variable, add it there, otherwise add as linear variable */
      if( SCIPhashmapExists(quadvaridxs, linvars[i]) )
      {
         var1pos = (int) (size_t) SCIPhashmapGetImage(quadvaridxs, linvars[i]);
         assert(consdata->quadvarterms[var1pos].var == linvars[i]);
         consdata->quadvarterms[var1pos].lincoef += lincoefs[i];
      }
      else
      {
         SCIP_CALL( addLinearCoef(scip, *cons, linvars[i], lincoefs[i]) );
      }
   }

   if( SCIPisTransformed(scip) )
   {
      SCIP_CONSHDLRDATA* conshdlrdata = SCIPconshdlrGetData(conshdlr);
      assert(conshdlrdata != NULL);
      assert(conshdlrdata->eventhdlr != NULL);

      SCIP_CALL( catchVarEvents(scip, conshdlrdata->eventhdlr, *cons) );
   }

   SCIPhashmapFree(&quadvaridxs);

   /* merge duplicate bilinear terms, move quad terms that are linear to linear vars */
   SCIP_CALL( mergeAndCleanBilinearTerms(scip, *cons) );
   SCIP_CALL( mergeAndCleanQuadVarTerms(scip, *cons) );
   SCIP_CALL( mergeAndCleanLinearVars(scip, *cons) );

   SCIPdebugMessage("created quadratic constraint ");
   SCIPdebugPrintCons(scip, *cons, NULL);

   if( SCIPgetStage(scip) == SCIP_STAGE_SOLVING )
   {
      SCIP_CALL( consInitsolQuadratic(scip, conshdlr, cons, 1) );
   }

   return SCIP_OKAY;
}

/** creates and captures a quadratic constraint with all its
 *  flags set to their default values.
 *
 *  The constraint should be given in the form
 *  \f[
 *  \ell \leq \sum_{i=1}^n b_i x_i + \sum_{j=1}^m a_j y_jz_j \leq u,
 *  \f]
 *  where \f$x_i = y_j = z_k\f$ is possible.
 *
 *  @note the constraint gets captured, hence at one point you have to release it using the method SCIPreleaseCons()
 */
SCIP_RETCODE SCIPcreateConsBasicQuadratic(
   SCIP*                 scip,               /**< SCIP data structure */
   SCIP_CONS**           cons,               /**< pointer to hold the created constraint */
   const char*           name,               /**< name of constraint */
   int                   nlinvars,           /**< number of linear terms (n) */
   SCIP_VAR**            linvars,            /**< array with variables in linear part (x_i) */
   SCIP_Real*            lincoefs,           /**< array with coefficients of variables in linear part (b_i) */
   int                   nquadterms,         /**< number of quadratic terms (m) */
   SCIP_VAR**            quadvars1,          /**< array with first variables in quadratic terms (y_j) */
   SCIP_VAR**            quadvars2,          /**< array with second variables in quadratic terms (z_j) */
   SCIP_Real*            quadcoefs,          /**< array with coefficients of quadratic terms (a_j) */
   SCIP_Real             lhs,                /**< left hand side of quadratic equation (ell) */
   SCIP_Real             rhs                 /**< right hand side of quadratic equation (u) */
   )
{
   SCIP_CALL( SCIPcreateConsQuadratic(scip, cons, name, nlinvars, linvars, lincoefs,
         nquadterms, quadvars1, quadvars2, quadcoefs, lhs, rhs,
         TRUE, TRUE, TRUE, TRUE, TRUE, FALSE, FALSE, FALSE, FALSE) );

   return SCIP_OKAY;
}

/** Creates and captures a quadratic constraint.
 * 
 * The constraint should be given in the form
 * \f[
 * \ell \leq \sum_{i=1}^n b_i x_i + \sum_{j=1}^m (a_j y_j^2 + b_j y_j) + \sum_{k=1}^p c_kv_kw_k \leq u.
 * \f]
 *
 *  @note the constraint gets captured, hence at one point you have to release it using the method SCIPreleaseCons()
 */
SCIP_RETCODE SCIPcreateConsQuadratic2(
   SCIP*                 scip,               /**< SCIP data structure */
   SCIP_CONS**           cons,               /**< pointer to hold the created constraint */
   const char*           name,               /**< name of constraint */
   int                   nlinvars,           /**< number of linear terms (n) */
   SCIP_VAR**            linvars,            /**< array with variables in linear part (x_i) */ 
   SCIP_Real*            lincoefs,           /**< array with coefficients of variables in linear part (b_i) */ 
   int                   nquadvarterms,      /**< number of quadratic terms (m) */
   SCIP_QUADVARTERM*     quadvarterms,       /**< quadratic variable terms */
   int                   nbilinterms,        /**< number of bilinear terms (p) */
   SCIP_BILINTERM*       bilinterms,         /**< bilinear terms */
   SCIP_Real             lhs,                /**< constraint left hand side (ell) */
   SCIP_Real             rhs,                /**< constraint right hand side (u) */
   SCIP_Bool             initial,            /**< should the LP relaxation of constraint be in the initial LP? */
   SCIP_Bool             separate,           /**< should the constraint be separated during LP processing? */
   SCIP_Bool             enforce,            /**< should the constraint be enforced during node processing? */
   SCIP_Bool             check,              /**< should the constraint be checked for feasibility? */
   SCIP_Bool             propagate,          /**< should the constraint be propagated during node processing? */
   SCIP_Bool             local,              /**< is constraint only valid locally? */
   SCIP_Bool             modifiable,         /**< is constraint modifiable (subject to column generation)? */
   SCIP_Bool             dynamic,            /**< is constraint dynamic? */
   SCIP_Bool             removable           /**< should the constraint be removed from the LP due to aging or cleanup? */
   )
{
   SCIP_CONSHDLR* conshdlr;
   SCIP_CONSDATA* consdata;

   assert(modifiable == FALSE); /* we do not support column generation */
   assert(nlinvars == 0 || (linvars != NULL && lincoefs != NULL));
   assert(nquadvarterms == 0 || quadvarterms != NULL);
   assert(nbilinterms == 0 || bilinterms != NULL);

   /* find the quadratic constraint handler */
   conshdlr = SCIPfindConshdlr(scip, CONSHDLR_NAME);
   if( conshdlr == NULL )
   {
      SCIPerrorMessage("quadratic constraint handler not found\n");
      return SCIP_PLUGINNOTFOUND;
   }

   /* create constraint data */
   SCIP_CALL( consdataCreate(scip, &consdata, lhs, rhs,
         nlinvars, linvars, lincoefs, nquadvarterms, quadvarterms, nbilinterms, bilinterms,
         TRUE) );

   /* create constraint */
   SCIP_CALL( SCIPcreateCons(scip, cons, name, conshdlr, consdata, initial, separate, enforce, check, propagate,
         local, modifiable, dynamic, removable, FALSE) );

   if( SCIPisTransformed(scip) )
   {
      SCIP_CONSHDLRDATA* conshdlrdata = SCIPconshdlrGetData(conshdlr);
      assert(conshdlrdata != NULL);
      assert(conshdlrdata->eventhdlr != NULL);

      SCIP_CALL( catchVarEvents(scip, conshdlrdata->eventhdlr, *cons) );
   }

   if( SCIPgetStage(scip) == SCIP_STAGE_SOLVING )
   {
      SCIP_CALL( consInitsolQuadratic(scip, conshdlr, cons, 1) );
   }

   return SCIP_OKAY;
}

/** creates and captures a quadratic constraint in its most basic version, i.e.,
 *  all constraint flags are set to their default values.
 *
 * The constraint should be given in the form
 * \f[
 * \ell \leq \sum_{i=1}^n b_i x_i + \sum_{j=1}^m (a_j y_j^2 + b_j y_j) + \sum_{k=1}^p c_kv_kw_k \leq u.
 * \f]
 *
 *  @note the constraint gets captured, hence at one point you have to release it using the method SCIPreleaseCons()
 */
SCIP_RETCODE SCIPcreateConsBasicQuadratic2(
   SCIP*                 scip,               /**< SCIP data structure */
   SCIP_CONS**           cons,               /**< pointer to hold the created constraint */
   const char*           name,               /**< name of constraint */
   int                   nlinvars,           /**< number of linear terms (n) */
   SCIP_VAR**            linvars,            /**< array with variables in linear part (x_i) */
   SCIP_Real*            lincoefs,           /**< array with coefficients of variables in linear part (b_i) */
   int                   nquadvarterms,      /**< number of quadratic terms (m) */
   SCIP_QUADVARTERM*     quadvarterms,       /**< quadratic variable terms */
   int                   nbilinterms,        /**< number of bilinear terms (p) */
   SCIP_BILINTERM*       bilinterms,         /**< bilinear terms */
   SCIP_Real             lhs,                /**< constraint left hand side (ell) */
   SCIP_Real             rhs                 /**< constraint right hand side (u) */
   )
{
   SCIP_CALL( SCIPcreateConsQuadratic2(scip, cons, name, nlinvars, linvars, lincoefs,
         nquadvarterms, quadvarterms, nbilinterms, bilinterms, lhs, rhs,
         TRUE, TRUE, TRUE, TRUE, TRUE, FALSE, FALSE, FALSE, FALSE) );

   return SCIP_OKAY;
}


/** Adds a constant to the constraint function, that is, subtracts a constant from both sides */
void SCIPaddConstantQuadratic(
   SCIP*                 scip,               /**< SCIP data structure */
   SCIP_CONS*            cons,               /**< constraint */
   SCIP_Real             constant            /**< constant to subtract from both sides */
   )
{
   SCIP_CONSDATA* consdata;

   assert(scip != NULL);
   assert(cons != NULL);
   assert(!SCIPisInfinity(scip, REALABS(constant)));

   consdata = SCIPconsGetData(cons);
   assert(consdata != NULL);
   assert(consdata->lhs <= consdata->rhs);

   if( !SCIPisInfinity(scip, -consdata->lhs) )
      consdata->lhs -= constant;
   if( !SCIPisInfinity(scip,  consdata->rhs) )
      consdata->rhs -= constant;

   if( consdata->lhs > consdata->rhs )
   {
      assert(SCIPisEQ(scip, consdata->lhs, consdata->rhs));
      consdata->lhs = consdata->rhs;
   }
}

/** Adds a linear variable with coefficient to a quadratic constraint.
 */
SCIP_RETCODE SCIPaddLinearVarQuadratic(
   SCIP*                 scip,               /**< SCIP data structure */
   SCIP_CONS*            cons,               /**< constraint */
   SCIP_VAR*             var,                /**< variable */
   SCIP_Real             coef                /**< coefficient of variable */
   )
{
   assert(scip != NULL);
   assert(cons != NULL);
   assert(var  != NULL);
   assert(!SCIPisInfinity(scip, REALABS(coef)));

   SCIP_CALL( addLinearCoef(scip, cons, var, coef) );

   return SCIP_OKAY;
}

/** Adds a quadratic variable with linear and square coefficient to a quadratic constraint.
 */
SCIP_RETCODE SCIPaddQuadVarQuadratic(
   SCIP*                 scip,               /**< SCIP data structure */
   SCIP_CONS*            cons,               /**< constraint */
   SCIP_VAR*             var,                /**< variable */
   SCIP_Real             lincoef,            /**< linear coefficient of variable */
   SCIP_Real             sqrcoef             /**< square coefficient of variable */
   )
{
   assert(scip != NULL);
   assert(cons != NULL);
   assert(var  != NULL);
   assert(!SCIPisInfinity(scip, REALABS(lincoef)));
   assert(!SCIPisInfinity(scip, REALABS(sqrcoef)));

   SCIP_CALL( addQuadVarTerm(scip, cons, var, lincoef, sqrcoef, SCIPconsIsTransformed(cons)) );

   return SCIP_OKAY;
}

/** Adds a linear coefficient for a quadratic variable.
 *
 * Variable will be added with square coefficient 0.0 if not existing yet.
 */
SCIP_RETCODE SCIPaddQuadVarLinearCoefQuadratic(
   SCIP*                 scip,               /**< SCIP data structure */
   SCIP_CONS*            cons,               /**< constraint */
   SCIP_VAR*             var,                /**< variable */
   SCIP_Real             coef                /**< value to add to linear coefficient of variable */
   )
{
   SCIP_CONSDATA* consdata;
   int pos;

   assert(scip != NULL);
   assert(cons != NULL);
   assert(var  != NULL);
   assert(!SCIPisInfinity(scip, REALABS(coef)));

   if( SCIPisZero(scip, coef) )
      return SCIP_OKAY;

   consdata = SCIPconsGetData(cons);
   assert(consdata != NULL);

   SCIP_CALL( consdataFindQuadVarTerm(scip, consdata, var, &pos) );
   if( pos < 0 )
   {
      SCIP_CALL( addQuadVarTerm(scip, cons, var, coef, 0.0, SCIPconsIsTransformed(cons)) );
      return SCIP_OKAY;
   }
   assert(pos < consdata->nquadvars);
   assert(consdata->quadvarterms[pos].var == var);

   consdata->quadvarterms[pos].lincoef += coef;

   /* update flags and invalid activities */
   consdata->ispropagated  = FALSE;
   consdata->ispresolved   = consdata->ispresolved && !SCIPisZero(scip, consdata->quadvarterms[pos].lincoef);

   SCIPintervalSetEmpty(&consdata->quadactivitybounds);
   consdata->activity = SCIP_INVALID;

   return SCIP_OKAY;
}

/** Adds a square coefficient for a quadratic variable.
 *
 * Variable will be added with linear coefficient 0.0 if not existing yet.
 */
SCIP_RETCODE SCIPaddSquareCoefQuadratic(
   SCIP*                 scip,               /**< SCIP data structure */
   SCIP_CONS*            cons,               /**< constraint */
   SCIP_VAR*             var,                /**< variable */
   SCIP_Real             coef                /**< value to add to square coefficient of variable */
   )
{
   SCIP_CONSDATA* consdata;
   int pos;

   assert(scip != NULL);
   assert(cons != NULL);
   assert(var  != NULL);
   assert(!SCIPisInfinity(scip, REALABS(coef)));

   if( SCIPisZero(scip, coef) )
      return SCIP_OKAY;

   consdata = SCIPconsGetData(cons);
   assert(consdata != NULL);

   SCIP_CALL( consdataFindQuadVarTerm(scip, consdata, var, &pos) );
   if( pos < 0 )
   {
      SCIP_CALL( addQuadVarTerm(scip, cons, var, 0.0, coef, SCIPconsIsTransformed(cons)) );
      return SCIP_OKAY;
   }
   assert(pos < consdata->nquadvars);
   assert(consdata->quadvarterms[pos].var == var);

   consdata->quadvarterms[pos].sqrcoef += coef;

   /* update flags and invalid activities */
   consdata->isconvex      = FALSE;
   consdata->isconcave     = FALSE;
   consdata->iscurvchecked = FALSE;
   consdata->ispropagated  = FALSE;
   consdata->ispresolved   = consdata->ispresolved && !SCIPisZero(scip, consdata->quadvarterms[pos].sqrcoef);

   SCIPintervalSetEmpty(&consdata->quadactivitybounds);
   consdata->activity = SCIP_INVALID;

   return SCIP_OKAY;
}

/** Adds a bilinear term to a quadratic constraint.
 *
 * Variables will be added with linear and square coefficient 0.0 if not existing yet.
 * If variables are equal, only the square coefficient of the variable is updated.
 */
SCIP_RETCODE SCIPaddBilinTermQuadratic(
   SCIP*                 scip,               /**< SCIP data structure */
   SCIP_CONS*            cons,               /**< constraint */
   SCIP_VAR*             var1,               /**< first variable */
   SCIP_VAR*             var2,               /**< second variable */
   SCIP_Real             coef                /**< coefficient of bilinear term */
   )
{
   SCIP_CONSDATA* consdata;
   int            var1pos;
   int            var2pos;

   assert(scip != NULL);
   assert(cons != NULL);
   assert(var1 != NULL);
   assert(var2 != NULL);
   assert(!SCIPisInfinity(scip, REALABS(coef)));

   if( var1 == var2 )
   {
      SCIP_CALL( SCIPaddSquareCoefQuadratic(scip, cons, var1, coef) );
      return SCIP_OKAY;
   }

   consdata = SCIPconsGetData(cons);
   assert(consdata != NULL);

   SCIP_CALL( consdataFindQuadVarTerm(scip, consdata, var1, &var1pos) );
   if( var1pos < 0 )
   {
      SCIP_CALL( addQuadVarTerm(scip, cons, var1, 0.0, 0.0, SCIPconsIsTransformed(cons)) );
      var1pos = consdata->nquadvars-1;
   }

   if( !consdata->quadvarssorted )
   {
      SCIP_CALL( consdataSortQuadVarTerms(scip, consdata) );
      /* sorting may change the position of var1 */
      SCIP_CALL( consdataFindQuadVarTerm(scip, consdata, var1, &var1pos) );
      assert(var1pos >= 0);
   }

   assert(consdata->quadvarssorted);
   SCIP_CALL( consdataFindQuadVarTerm(scip, consdata, var2, &var2pos) );
   if( var2pos < 0 )
   {
      SCIP_CALL( addQuadVarTerm(scip, cons, var2, 0.0, 0.0, SCIPconsIsTransformed(cons)) );
      var2pos = consdata->nquadvars-1;
   }

   assert(consdata->quadvarterms[var1pos].var == var1);
   assert(consdata->quadvarterms[var2pos].var == var2);

   SCIP_CALL( addBilinearTerm(scip, cons, var1pos, var2pos, coef) );

   return SCIP_OKAY;
}

/** Gets the quadratic constraint as a nonlinear row representation.
 */
SCIP_RETCODE SCIPgetNlRowQuadratic(
   SCIP*                 scip,               /**< SCIP data structure */
   SCIP_CONS*            cons,               /**< constraint */
   SCIP_NLROW**          nlrow               /**< pointer to store nonlinear row */
   )
{
   SCIP_CONSDATA* consdata;

   assert(cons  != NULL);
   assert(nlrow != NULL);

   consdata = SCIPconsGetData(cons);
   assert(consdata != NULL);

   if( consdata->nlrow == NULL )
   {
      SCIP_CALL( createNlRow(scip, cons) );
   }
   assert(consdata->nlrow != NULL);
   *nlrow = consdata->nlrow;

   return SCIP_OKAY;
}

/** Gets the number of variables in the linear term of a quadratic constraint.
 */
int SCIPgetNLinearVarsQuadratic(
   SCIP*                 scip,               /**< SCIP data structure */
   SCIP_CONS*            cons                /**< constraint */
   )
{
   assert(cons != NULL);
   assert(SCIPconsGetData(cons) != NULL);

   return SCIPconsGetData(cons)->nlinvars;
}

/** Gets the variables in the linear part of a quadratic constraint.
 *  Length is given by SCIPgetNLinearVarsQuadratic.
 */
SCIP_VAR** SCIPgetLinearVarsQuadratic(
   SCIP*                 scip,               /**< SCIP data structure */
   SCIP_CONS*            cons                /**< constraint */
   )
{
   assert(cons != NULL);
   assert(SCIPconsGetData(cons) != NULL);

   return SCIPconsGetData(cons)->linvars;
}

/** Gets the coefficients in the linear part of a quadratic constraint.
 *  Length is given by SCIPgetNLinearVarsQuadratic.
 */
SCIP_Real* SCIPgetCoefsLinearVarsQuadratic(
   SCIP*                 scip,               /**< SCIP data structure */
   SCIP_CONS*            cons                /**< constraint */
   )
{
   assert(cons != NULL);
   assert(SCIPconsGetData(cons) != NULL);

   return SCIPconsGetData(cons)->lincoefs;
}

/** Gets the number of quadratic variable terms of a quadratic constraint.
 */
int SCIPgetNQuadVarTermsQuadratic(
   SCIP*                 scip,               /**< SCIP data structure */
   SCIP_CONS*            cons                /**< constraint */
   )
{
   assert(cons != NULL);
   assert(SCIPconsGetData(cons) != NULL);

   return SCIPconsGetData(cons)->nquadvars;
}

/** Gets the quadratic variable terms of a quadratic constraint.
 *  Length is given by SCIPgetNQuadVarTermsQuadratic.
 */
SCIP_QUADVARTERM* SCIPgetQuadVarTermsQuadratic(
   SCIP*                 scip,               /**< SCIP data structure */
   SCIP_CONS*            cons                /**< constraint */
   )
{
   assert(cons != NULL);
   assert(SCIPconsGetData(cons) != NULL);

   return SCIPconsGetData(cons)->quadvarterms;
}

/** Ensures that quadratic variable terms are sorted. */
SCIP_RETCODE SCIPsortQuadVarTermsQuadratic(
   SCIP*                 scip,               /**< SCIP data structure */
   SCIP_CONS*            cons                /**< constraint */
   )
{
   assert(cons != NULL);
   assert(SCIPconsGetData(cons) != NULL);

   SCIP_CALL( consdataSortQuadVarTerms(scip, SCIPconsGetData(cons)) );

   return SCIP_OKAY;
}

/** Finds the position of a quadratic variable term for a given variable.
 *
 * @note If the quadratic variable terms have not been sorted before, then a search may reorder the current order of the terms.
 */
SCIP_RETCODE SCIPfindQuadVarTermQuadratic(
   SCIP*                 scip,               /**< SCIP data structure */
   SCIP_CONS*            cons,               /**< constraint */
   SCIP_VAR*             var,                /**< variable to search for */
   int*                  pos                 /**< buffer to store position of quadvarterm for var, or -1 if not found */
   )
{
   assert(cons != NULL);
   assert(SCIPconsGetData(cons) != NULL);
   assert(var != NULL);
   assert(pos != NULL);

   SCIP_CALL( consdataFindQuadVarTerm(scip, SCIPconsGetData(cons), var, pos) );

   return SCIP_OKAY;
}

/** Gets the number of bilinear terms of a quadratic constraint.
 */
int SCIPgetNBilinTermsQuadratic(
   SCIP*                 scip,               /**< SCIP data structure */
   SCIP_CONS*            cons                /**< constraint */
   )
{
   assert(cons != NULL);
   assert(SCIPconsGetData(cons) != NULL);

   return SCIPconsGetData(cons)->nbilinterms;
}

/** Gets the bilinear terms of a quadratic constraint.
 *  Length is given by SCIPgetNBilinTermQuadratic.
 */
SCIP_BILINTERM* SCIPgetBilinTermsQuadratic(
   SCIP*                 scip,               /**< SCIP data structure */
   SCIP_CONS*            cons                /**< constraint */
   )
{
   assert(cons != NULL);
   assert(SCIPconsGetData(cons) != NULL);

   return SCIPconsGetData(cons)->bilinterms;
}

/** Gets the left hand side of a quadratic constraint.
 */
SCIP_Real SCIPgetLhsQuadratic(
   SCIP*                 scip,               /**< SCIP data structure */
   SCIP_CONS*            cons                /**< constraint */
   )
{
   assert(cons != NULL);
   assert(SCIPconsGetData(cons) != NULL);

   return SCIPconsGetData(cons)->lhs;
}

/** Gets the right hand side of a quadratic constraint.
 */
SCIP_Real SCIPgetRhsQuadratic(
   SCIP*                 scip,               /**< SCIP data structure */
   SCIP_CONS*            cons                /**< constraint */
   )
{
   assert(cons != NULL);
   assert(SCIPconsGetData(cons) != NULL);

   return SCIPconsGetData(cons)->rhs;
}

/** Check the quadratic function of a quadratic constraint for its semi-definiteness, if not done yet.
 */
SCIP_RETCODE SCIPcheckCurvatureQuadratic(
   SCIP*                 scip,               /**< SCIP data structure */
   SCIP_CONS*            cons                /**< constraint */
   )
{
   assert(cons != NULL);

   SCIP_CALL( checkCurvature(scip, cons, TRUE) );

   return SCIP_OKAY;
}

/** Indicates whether the quadratic function of a quadratic constraint is (known to be) convex.
 */
SCIP_Bool SCIPisConvexQuadratic(
   SCIP*                 scip,               /**< SCIP data structure */
   SCIP_CONS*            cons                /**< constraint */
   )
{
   SCIP_Bool determined;

   assert(cons != NULL);
   assert(SCIPconsGetData(cons) != NULL);

   checkCurvatureEasy(scip, cons, &determined, FALSE);
   assert(determined);

   return (SCIPconsGetData(cons)->isconvex);
}

/** Indicates whether the quadratic function of a quadratic constraint is (known to be) concave.
 */
SCIP_Bool SCIPisConcaveQuadratic(
   SCIP*                 scip,               /**< SCIP data structure */
   SCIP_CONS*            cons                /**< constraint */
   )
{
   SCIP_Bool determined;

   assert(cons != NULL);
   assert(SCIPconsGetData(cons) != NULL);

   checkCurvatureEasy(scip, cons, &determined, FALSE);
   assert(determined);

   return (SCIPconsGetData(cons)->isconcave);
}

/** Computes the violation of a constraint by a solution */
SCIP_RETCODE SCIPgetViolationQuadratic(
   SCIP*                 scip,               /**< SCIP data structure */
   SCIP_CONS*            cons,               /**< constraint */
   SCIP_SOL*             sol,                /**< solution which violation to calculate, or NULL for LP solution */
   SCIP_Real*            violation           /**< pointer to store violation of constraint */
   )
{
   SCIP_CONSHDLR* conshdlr;
   SCIP_CONSDATA* consdata;

   assert(scip != NULL);
   assert(cons != NULL);
   assert(violation != NULL);

   conshdlr = SCIPconsGetHdlr(cons);
   assert(conshdlr != NULL);

   SCIP_CALL( computeViolation(scip, conshdlr, cons, sol) );

   consdata = SCIPconsGetData(cons);
   assert(consdata != NULL);

   *violation = MAX(consdata->lhsviol, consdata->rhsviol);

   return SCIP_OKAY;
}

/** Indicates whether the quadratic constraint is local w.r.t. the current local bounds.
 *
 * That is, checks whether each variable with a square term is fixed and for each bilinear term at least one variable is fixed.
 */
SCIP_Bool SCIPisLinearLocalQuadratic(
   SCIP*                 scip,               /**< SCIP data structure */
   SCIP_CONS*            cons                /**< constraint */
)
{
   SCIP_CONSDATA* consdata;
   SCIP_VAR* var1;
   SCIP_VAR* var2;
   int i;

   assert(scip != NULL);
   assert(cons != NULL);

   consdata = SCIPconsGetData(cons);
   assert(consdata != NULL);

   /* check all square terms */
   for( i = 0; i < consdata->nquadvars; ++i )
   {
      if( consdata->quadvarterms[i].sqrcoef == 0.0 )
         continue;

      var1 = consdata->quadvarterms[i].var;
      assert(var1 != NULL);

      if( !SCIPisRelEQ(scip, SCIPvarGetLbLocal(var1), SCIPvarGetUbLocal(var1)) )
         return FALSE;
   }

   for( i = 0; i < consdata->nbilinterms; ++i )
   {
      var1 = consdata->bilinterms[i].var1;
      var2 = consdata->bilinterms[i].var2;

      assert(var1 != NULL);
      assert(var2 != NULL);

      if( !SCIPisRelEQ(scip, SCIPvarGetLbLocal(var1), SCIPvarGetUbLocal(var1)) &&
         ! SCIPisRelEQ(scip, SCIPvarGetLbLocal(var2), SCIPvarGetUbLocal(var2)) )
         return FALSE;
   }

   return TRUE;
}

/** Adds the constraint to an NLPI problem. */
SCIP_RETCODE SCIPaddToNlpiProblemQuadratic(
   SCIP*                 scip,               /**< SCIP data structure */
   SCIP_CONS*            cons,               /**< constraint */
   SCIP_NLPI*            nlpi,               /**< interface to NLP solver */
   SCIP_NLPIPROBLEM*     nlpiprob,           /**< NLPI problem where to add constraint */
   SCIP_HASHMAP*         scipvar2nlpivar,    /**< mapping from SCIP variables to variable indices in NLPI */
   SCIP_Bool             names               /**< whether to pass constraint names to NLPI */
   )
{
   SCIP_CONSDATA* consdata;
   int            nlininds;
   int*           lininds;
   SCIP_Real*     linvals;
   int            nquadelems;
   SCIP_QUADELEM* quadelems;
   SCIP_VAR*      othervar;
   const char*    name;
   int            j;
   int            l;
   int            lincnt;
   int            quadcnt;
   int            idx1;
   int            idx2;

   assert(scip != NULL);
   assert(cons != NULL);
   assert(nlpi != NULL);
   assert(nlpiprob != NULL);
   assert(scipvar2nlpivar != NULL);

   consdata = SCIPconsGetData(cons);
   assert(consdata != NULL);

   /* count nonzeros in quadratic part */
   nlininds = consdata->nlinvars;
   nquadelems = consdata->nbilinterms;
   for( j = 0; j < consdata->nquadvars; ++j )
   {
      if( consdata->quadvarterms[j].sqrcoef != 0.0 )
         ++nquadelems;
      if( consdata->quadvarterms[j].lincoef != 0.0 )
         ++nlininds;
   }

   /* setup linear part */
   lininds = NULL;
   linvals = NULL;
   lincnt  = 0;
   if( nlininds > 0 )
   {
      SCIP_CALL( SCIPallocBufferArray(scip, &lininds, nlininds) );
      SCIP_CALL( SCIPallocBufferArray(scip, &linvals, nlininds) );

      for( j = 0; j < consdata->nlinvars; ++j )
      {
         linvals[j] = consdata->lincoefs[j];
         assert(SCIPhashmapExists(scipvar2nlpivar, consdata->linvars[j]));
         lininds[j] = (int) (size_t) SCIPhashmapGetImage(scipvar2nlpivar, consdata->linvars[j]);
      }

      lincnt = consdata->nlinvars;
   }

   /* setup quadratic part */
   quadelems = NULL;
   if( nquadelems > 0 )
   {
      SCIP_CALL( SCIPallocBufferArray(scip, &quadelems, nquadelems) );
   }
   quadcnt = 0;

   for( j = 0; j < consdata->nquadvars; ++j )
   {
      assert(SCIPhashmapExists(scipvar2nlpivar, consdata->quadvarterms[j].var));
      idx1 = (int)(size_t)SCIPhashmapGetImage(scipvar2nlpivar, consdata->quadvarterms[j].var);
      if( consdata->quadvarterms[j].lincoef != 0.0 )
      {
         assert(lininds != NULL);
         assert(linvals != NULL);
         lininds[lincnt] = idx1;
         linvals[lincnt] = consdata->quadvarterms[j].lincoef;
         ++lincnt;
      }

      if( consdata->quadvarterms[j].sqrcoef != 0.0 )
      {
         assert(quadcnt < nquadelems);
         assert(quadelems != NULL);
         quadelems[quadcnt].idx1 = idx1;
         quadelems[quadcnt].idx2 = idx1;
         quadelems[quadcnt].coef = consdata->quadvarterms[j].sqrcoef;
         ++quadcnt;
      }

      for( l = 0; l < consdata->quadvarterms[j].nadjbilin; ++l )
      {
         othervar = consdata->bilinterms[consdata->quadvarterms[j].adjbilin[l]].var2;
         /* if othervar is on position 2, then we process this bilinear term later (or it was processed already) */
         if( othervar == consdata->quadvarterms[j].var )
            continue;

         assert(quadcnt < nquadelems);
         assert(quadelems != NULL);
         assert(SCIPhashmapExists(scipvar2nlpivar, othervar));
         idx2 = (int)(size_t)SCIPhashmapGetImage(scipvar2nlpivar, othervar);
         quadelems[quadcnt].idx1 = MIN(idx1, idx2);
         quadelems[quadcnt].idx2 = MAX(idx1, idx2);
         quadelems[quadcnt].coef = consdata->bilinterms[consdata->quadvarterms[j].adjbilin[l]].coef;
         ++quadcnt;
      }
   }

   assert(quadcnt == nquadelems);
   assert(lincnt  == nlininds);

   name = names ? SCIPconsGetName(cons) : NULL;

   SCIP_CALL( SCIPnlpiAddConstraints(nlpi, nlpiprob, 1,
         &consdata->lhs, &consdata->rhs,
         &nlininds, &lininds, &linvals ,
         &nquadelems, &quadelems,
         NULL, NULL, &name) );

   SCIPfreeBufferArrayNull(scip, &quadelems);
   SCIPfreeBufferArrayNull(scip, &lininds);
   SCIPfreeBufferArrayNull(scip, &linvals);

   return SCIP_OKAY;
}