
constraint handler for nonlinear constraints
 Author
 Stefan Vigerske
This constraint handler handles constraints of the form
where and are coefficients and are nonlinear functions (given as expression tree).
Constraints are enforced by separation, domain propagation, and spatial branching.
For convex or concave , cuts that separate on the convex hull of the function graph are implemented. For that are not known to be convex or concave, a simple variant of linear estimation based on interval gradients is implemented.
Branching is performed for variables in nonconvex terms, if the relaxation solution cannot be separated.
This header offers the upgrade functionality to upgrade a general nonlinear constraint into a more specific constraint via SCIP_DECL_NONLINCONSUPGD().
Furthermore, the definition of callbacks used to reformulate an expression graph is offered by SCIP_DECL_EXPRGRAPHNODEREFORM().
Further, the function representation is stored in an expression graph, which allows to propagate variable domains and constraint sides and offers a simple convexity check. During presolve, the expression graph is reformulated, whereby new variables and constraints are created such that for the remaining nonlinear constraints the functions are known to be convex or concave. See also
 Stefan Vigerske
Decomposition of Multistage Stochastic Programs and a Constraint Integer Programming Approach to MixedInteger Nonlinear Programming
PhD Thesis, HumboldtUniversity Berlin, 2012, submitted.
Definition in file cons_nonlinear.h.
Go to the source code of this file.

SCIP_RETCODE  SCIPincludeConshdlrNonlinear (SCIP *scip) 

SCIP_RETCODE  SCIPincludeNonlinconsUpgrade (SCIP *scip, SCIP_DECL_NONLINCONSUPGD((*nonlinconsupgd)), SCIP_DECL_EXPRGRAPHNODEREFORM((*nodereform)), int priority, SCIP_Bool active, const char *conshdlrname) 

SCIP_RETCODE  SCIPcreateConsNonlinear (SCIP *scip, SCIP_CONS **cons, const char *name, int nlinvars, SCIP_VAR **linvars, SCIP_Real *lincoefs, int nexprtrees, SCIP_EXPRTREE **exprtrees, SCIP_Real *nonlincoefs, SCIP_Real lhs, SCIP_Real rhs, SCIP_Bool initial, SCIP_Bool separate, SCIP_Bool enforce, SCIP_Bool check, SCIP_Bool propagate, SCIP_Bool local, SCIP_Bool modifiable, SCIP_Bool dynamic, SCIP_Bool removable, SCIP_Bool stickingatnode) 

SCIP_RETCODE  SCIPcreateConsBasicNonlinear (SCIP *scip, SCIP_CONS **cons, const char *name, int nlinvars, SCIP_VAR **linvars, SCIP_Real *lincoefs, int nexprtrees, SCIP_EXPRTREE **exprtrees, SCIP_Real *nonlincoefs, SCIP_Real lhs, SCIP_Real rhs) 

SCIP_RETCODE  SCIPcreateConsNonlinear2 (SCIP *scip, SCIP_CONS **cons, const char *name, int nlinvars, SCIP_VAR **linvars, SCIP_Real *lincoefs, SCIP_EXPRGRAPHNODE *exprgraphnode, SCIP_Real lhs, SCIP_Real rhs, SCIP_Bool initial, SCIP_Bool separate, SCIP_Bool enforce, SCIP_Bool check, SCIP_Bool propagate, SCIP_Bool local, SCIP_Bool modifiable, SCIP_Bool dynamic, SCIP_Bool removable, SCIP_Bool stickingatnode) 

SCIP_RETCODE  SCIPcreateConsBasicNonlinear2 (SCIP *scip, SCIP_CONS **cons, const char *name, int nlinvars, SCIP_VAR **linvars, SCIP_Real *lincoefs, SCIP_EXPRGRAPHNODE *exprgraphnode, SCIP_Real lhs, SCIP_Real rhs) 

SCIP_RETCODE  SCIPaddLinearVarNonlinear (SCIP *scip, SCIP_CONS *cons, SCIP_VAR *var, SCIP_Real coef) 

SCIP_RETCODE  SCIPsetExprtreesNonlinear (SCIP *scip, SCIP_CONS *cons, int nexprtrees, SCIP_EXPRTREE **exprtrees, SCIP_Real *coefs) 

SCIP_RETCODE  SCIPaddExprtreesNonlinear (SCIP *scip, SCIP_CONS *cons, int nexprtrees, SCIP_EXPRTREE **exprtrees, SCIP_Real *coefs) 

SCIP_RETCODE  SCIPgetNlRowNonlinear (SCIP *scip, SCIP_CONS *cons, SCIP_NLROW **nlrow) 

int  SCIPgetNLinearVarsNonlinear (SCIP *scip, SCIP_CONS *cons) 

SCIP_VAR **  SCIPgetLinearVarsNonlinear (SCIP *scip, SCIP_CONS *cons) 

SCIP_Real *  SCIPgetLinearCoefsNonlinear (SCIP *scip, SCIP_CONS *cons) 

int  SCIPgetNExprtreesNonlinear (SCIP *scip, SCIP_CONS *cons) 

SCIP_EXPRTREE **  SCIPgetExprtreesNonlinear (SCIP *scip, SCIP_CONS *cons) 

SCIP_Real *  SCIPgetExprtreeCoefsNonlinear (SCIP *scip, SCIP_CONS *cons) 

SCIP_EXPRGRAPHNODE *  SCIPgetExprgraphNodeNonlinear (SCIP *scip, SCIP_CONS *cons) 

SCIP_Real  SCIPgetLhsNonlinear (SCIP *scip, SCIP_CONS *cons) 

SCIP_Real  SCIPgetRhsNonlinear (SCIP *scip, SCIP_CONS *cons) 

SCIP_RETCODE  SCIPcheckCurvatureNonlinear (SCIP *scip, SCIP_CONS *cons) 

SCIP_RETCODE  SCIPgetCurvatureNonlinear (SCIP *scip, SCIP_CONS *cons, SCIP_Bool checkcurv, SCIP_EXPRCURV *curvature) 

SCIP_RETCODE  SCIPgetExprtreeCurvaturesNonlinear (SCIP *scip, SCIP_CONS *cons, SCIP_Bool checkcurv, SCIP_EXPRCURV **curvatures) 

SCIP_RETCODE  SCIPgetViolationNonlinear (SCIP *scip, SCIP_CONS *cons, SCIP_SOL *sol, SCIP_Real *violation) 

SCIP_EXPRGRAPH *  SCIPgetExprgraphNonlinear (SCIP *scip, SCIP_CONSHDLR *conshdlr) 

#define SCIP_DECL_NONLINCONSUPGD 
( 

x  ) 

Value:
int* nupgdconss, SCIP_CONS** upgdconss, int upgdconsssize)
struct SCIP_Cons SCIP_CONS
enum SCIP_Retcode SCIP_RETCODE
upgrading method for nonlinear constraints into more specific constraints
the method might upgrade a nonlinear constraint into a set of upgrade constraints the caller provided an array upgdconss to store upgrade constraints the length of upgdconss is given by upgdconsssize if an upgrade is not possible, set *nupgdconss to zero if more than upgdconsssize many constraints shall replace cons, the function should return the required number as negated value in *nupgdconss i.e., if cons should be replaced by 3 constraints, the function should set *nupgdconss to 3 and return with SCIP_OKAY
input:
 scip : SCIP main data structure
 cons : the nonlinear constraint to upgrade
 nupgdconss : pointer to store number of constraints that replace this constraint
 upgdconss : array to store constraints that replace this constraint
 upgdconsssize : length of the provided upgdconss array
Definition at line 82 of file cons_nonlinear.h.
#define SCIP_DECL_EXPRGRAPHNODEREFORM 
( 

x  ) 

Value:
enum SCIP_Retcode SCIP_RETCODE
struct SCIP_ExprGraph SCIP_EXPRGRAPH
struct SCIP_ExprGraphNode SCIP_EXPRGRAPHNODE
reformulation method for expression graph nodes
The method might reformulate a node in an expression graph by adding auxiliary constraints and/or variables. The caller provided an expression graph node which is to be reformulated. If the method takes action, it has to return the node that should replace the given node in *reformnode. The caller will then ensure that all parents of node will use *reformnode, so node may be freed. If the method does not do any reformulation, it shall return NULL in *reformnode. The counter naddcons can be used to setup the names of added variables/constraints. The method should increase this counter by the number of added constraints. The method has to ensure that the reformulated node, if still valid, has valid bound and curvature information.
input:
 scip : SCIP main data structure
 exprgraph : the expression graph which node to reformulate
 node : the expression graph node to reformulate
 naddcons : counter on number of added constraints so far
output:
 naddcons : to be increased by number of additionally added constraints
 reformnode : reformulated node to replace node with, or NULL if no reformulation
Definition at line 109 of file cons_nonlinear.h.
creates the handler for nonlinear constraints and includes it in SCIP
 Parameters

includes a nonlinear constraint upgrade method into the nonlinear constraint handler
 Parameters

scip  SCIP data structure 
priority  priority of upgrading method 
active  should the upgrading method by active by default? 
conshdlrname  name of the constraint handler 
SCIP_RETCODE SCIPcreateConsNonlinear 
( 
SCIP * 
scip, 


SCIP_CONS ** 
cons, 


const char * 
name, 


int 
nlinvars, 


SCIP_VAR ** 
linvars, 


SCIP_Real * 
lincoefs, 


int 
nexprtrees, 


SCIP_EXPRTREE ** 
exprtrees, 


SCIP_Real * 
nonlincoefs, 


SCIP_Real 
lhs, 


SCIP_Real 
rhs, 


SCIP_Bool 
initial, 


SCIP_Bool 
separate, 


SCIP_Bool 
enforce, 


SCIP_Bool 
check, 


SCIP_Bool 
propagate, 


SCIP_Bool 
local, 


SCIP_Bool 
modifiable, 


SCIP_Bool 
dynamic, 


SCIP_Bool 
removable, 


SCIP_Bool 
stickingatnode 

) 
 
creates and captures a nonlinear constraint this variant takes expression trees as input
 Note
 the constraint gets captured, hence at one point you have to release it using the method SCIPreleaseCons()
 Parameters

scip  SCIP data structure 
cons  pointer to hold the created constraint 
name  name of constraint 
nlinvars  number of linear variables in the constraint 
linvars  array with linear variables of constraint entries 
lincoefs  array with coefficients of constraint linear entries 
nexprtrees  number of expression trees for nonlinear part of constraint 
exprtrees  expression trees for nonlinear part of constraint 
nonlincoefs  coefficients for expression trees for nonlinear part, or NULL if all 1.0 
lhs  left hand side of constraint 
rhs  right hand side of constraint 
initial  should the LP relaxation of constraint be in the initial LP? Usually set to TRUE. Set to FALSE for 'lazy constraints'. 
separate  should the constraint be separated during LP processing? Usually set to TRUE. 
enforce  should the constraint be enforced during node processing? TRUE for model constraints, FALSE for additional, redundant constraints. 
check  should the constraint be checked for feasibility? TRUE for model constraints, FALSE for additional, redundant constraints. 
propagate  should the constraint be propagated during node processing? Usually set to TRUE. 
local  is constraint only valid locally? Usually set to FALSE. Has to be set to TRUE, e.g., for branching constraints. 
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. 
dynamic  is constraint subject to aging? Usually set to FALSE. Set to TRUE for own cuts which are seperated as constraints. 
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'. 
stickingatnode  should the constraint always be kept at the node where it was added, even if it may be moved to a more global node? Usually set to FALSE. Set to TRUE to for constraints that represent node data. 
SCIP_RETCODE SCIPcreateConsBasicNonlinear 
( 
SCIP * 
scip, 


SCIP_CONS ** 
cons, 


const char * 
name, 


int 
nlinvars, 


SCIP_VAR ** 
linvars, 


SCIP_Real * 
lincoefs, 


int 
nexprtrees, 


SCIP_EXPRTREE ** 
exprtrees, 


SCIP_Real * 
nonlincoefs, 


SCIP_Real 
lhs, 


SCIP_Real 
rhs 

) 
 
creates and captures a nonlinear constraint in its most basic version, i. e., all constraint flags are set to their basic value as explained for the method SCIPcreateConsNonlinear(); all flags can be set via SCIPsetConsFLAGNAMEmethods in scip.h
this variant takes expression trees as input
 See Also
 SCIPcreateConsNonlinear() for information about the basic constraint flag configuration
 Note
 the constraint gets captured, hence at one point you have to release it using the method SCIPreleaseCons()
 Parameters

scip  SCIP data structure 
cons  pointer to hold the created constraint 
name  name of constraint 
nlinvars  number of linear variables in the constraint 
linvars  array with linear variables of constraint entries 
lincoefs  array with coefficients of constraint linear entries 
nexprtrees  number of expression trees for nonlinear part of constraint 
exprtrees  expression trees for nonlinear part of constraint 
nonlincoefs  coefficients for expression trees for nonlinear part, or NULL if all 1.0 
lhs  left hand side of constraint 
rhs  right hand side of constraint 
SCIP_RETCODE SCIPcreateConsNonlinear2 
( 
SCIP * 
scip, 


SCIP_CONS ** 
cons, 


const char * 
name, 


int 
nlinvars, 


SCIP_VAR ** 
linvars, 


SCIP_Real * 
lincoefs, 


SCIP_EXPRGRAPHNODE * 
exprgraphnode, 


SCIP_Real 
lhs, 


SCIP_Real 
rhs, 


SCIP_Bool 
initial, 


SCIP_Bool 
separate, 


SCIP_Bool 
enforce, 


SCIP_Bool 
check, 


SCIP_Bool 
propagate, 


SCIP_Bool 
local, 


SCIP_Bool 
modifiable, 


SCIP_Bool 
dynamic, 


SCIP_Bool 
removable, 


SCIP_Bool 
stickingatnode 

) 
 
creates and captures a nonlinear constraint this variant takes a node of the expression graph as input and can only be used during presolving it is assumed that the nonlinear constraint will be added to the transformed problem short after creation the given exprgraphnode is captured in this method
 Note
 the constraint gets captured, hence at one point you have to release it using the method SCIPreleaseCons()
 Parameters

scip  SCIP data structure 
cons  pointer to hold the created constraint 
name  name of constraint 
nlinvars  number of linear variables in the constraint 
linvars  array with linear variables of constraint entries 
lincoefs  array with coefficients of constraint linear entries 
exprgraphnode  expression graph node associated to nonlinear expression 
lhs  left hand side of constraint 
rhs  right hand side of constraint 
initial  should the LP relaxation of constraint be in the initial LP? Usually set to TRUE. Set to FALSE for 'lazy constraints'. 
separate  should the constraint be separated during LP processing? Usually set to TRUE. 
enforce  should the constraint be enforced during node processing? TRUE for model constraints, FALSE for additional, redundant constraints. 
check  should the constraint be checked for feasibility? TRUE for model constraints, FALSE for additional, redundant constraints. 
propagate  should the constraint be propagated during node processing? Usually set to TRUE. 
local  is constraint only valid locally? Usually set to FALSE. Has to be set to TRUE, e.g., for branching constraints. 
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. 
dynamic  is constraint subject to aging? Usually set to FALSE. Set to TRUE for own cuts which are seperated as constraints. 
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'. 
stickingatnode  should the constraint always be kept at the node where it was added, even if it may be moved to a more global node? Usually set to FALSE. Set to TRUE to for constraints that represent node data. 
creates and captures a nonlinear constraint in its most basic version, i. e., all constraint flags are set to their basic value as explained for the method SCIPcreateConsNonlinear2(); all flags can be set via SCIPsetConsFLAGNAMEmethods in scip.h
this variant takes a node of the expression graph as input and can only be used during presolving it is assumed that the nonlinear constraint will be added to the transformed problem short after creation the given exprgraphnode is captured in this method
 See Also
 SCIPcreateConsNonlinear2() for information about the basic constraint flag configuration
 Note
 the constraint gets captured, hence at one point you have to release it using the method SCIPreleaseCons()
 Parameters

scip  SCIP data structure 
cons  pointer to hold the created constraint 
name  name of constraint 
nlinvars  number of linear variables in the constraint 
linvars  array with linear variables of constraint entries 
lincoefs  array with coefficients of constraint linear entries 
exprgraphnode  expression graph node associated to nonlinear expression 
lhs  left hand side of constraint 
rhs  right hand side of constraint 
adds a linear variable with coefficient to a nonlinear constraint
 Parameters

scip  SCIP data structure 
cons  constraint 
var  variable 
coef  coefficient of variable 
sets the expression trees in a nonlinear constraint constraint must not be active yet
 Parameters

scip  SCIP data structure 
cons  constraint 
nexprtrees  number of expression trees 
exprtrees  new expression trees, or NULL if nexprtrees is 0 
coefs  coefficients of expression trees, or NULL if all 1.0 
adds expression trees to a nonlinear constraint constraint must not be active yet
 Parameters

scip  SCIP data structure 
cons  constraint 
nexprtrees  number of expression trees 
exprtrees  new expression trees, or NULL if nexprtrees is 0 
coefs  coefficients of expression trees, or NULL if all 1.0 
gets the nonlinear constraint as a nonlinear row representation
 Parameters

scip  SCIP data structure 
cons  constraint 
nlrow  pointer to store nonlinear row 
int SCIPgetNLinearVarsNonlinear 
( 
SCIP * 
scip, 


SCIP_CONS * 
cons 

) 
 
gets the number of variables in the linear term of a nonlinear constraint
 Parameters

scip  SCIP data structure 
cons  constraint 
gets the variables in the linear part of a nonlinear constraint
 Parameters

scip  SCIP data structure 
cons  constraint 
gets the coefficients in the linear part of a nonlinear constraint
 Parameters

scip  SCIP data structure 
cons  constraint 
gets the number of expression trees of a nonlinear constraint
 Parameters

scip  SCIP data structure 
cons  constraint 
gets the expression trees of a nonlinear constraint
 Parameters

scip  SCIP data structure 
cons  constraint 
gets the coefficients of the expression trees of a nonlinear constraint
 Parameters

scip  SCIP data structure 
cons  constraint 
gets the expression graph node of a nonlinear constraint
 Parameters

scip  SCIP data structure 
cons  constraint 
gets the left hand side of a nonlinear constraint
 Parameters

scip  SCIP data structure 
cons  constraint 
gets the right hand side of a nonlinear constraint
 Parameters

scip  SCIP data structure 
cons  constraint 
check the function of a nonlinear constraint for convexity/concavity, if not done yet
 Parameters

scip  SCIP data structure 
cons  constraint 
gets the curvature of the nonlinear function of a nonlinear constraint
The curvature is computed by summing up the curvature for each nonlinear summand. To get the curvature for single summands, use SCIPgetExprtreeCurvaturesNonlinear().
 Parameters

scip  SCIP data structure 
cons  constraint 
checkcurv  whether to check constraint curvature, if not checked before 
curvature  pointer to store curvature of constraint 
gets the curvature of the expression trees (multiplied by their coefficient) of a nonlinear constraint
 Parameters

scip  SCIP data structure 
cons  constraint 
checkcurv  whether to check constraint curvature, if not checked before 
curvatures  buffer to store curvatures of exprtrees 
computes the violation of a nonlinear constraint by a solution
 Parameters

scip  SCIP data structure 
cons  constraint 
sol  solution which violation to calculate, or NULL for LP solution 
violation  pointer to store violation of constraint 
gets expression graph of nonlinear constraint handler
 Parameters

scip  SCIP data structure 
conshdlr  nonlinear constraint handler 
