expr_pow.h

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/**@file   expr_pow.h
 * @ingroup EXPRHDLRS
 * @brief  power and signed power expression handlers
 * @author Benjamin Mueller
 */

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

#ifndef __SCIP_EXPR_POW_H__
#define __SCIP_EXPR_POW_H__

#include "scip/scip.h"
#include "scip/type_expr.h"

#ifdef __cplusplus
extern "C" {
#endif

/**@addtogroup EXPRHDLRS
 *
 * @{
 *
 * @name Power and signed power expression
 *
 * These expression handlers provide the power function, that is,
 * \f[
 *   x \mapsto \begin{cases}
 *     x^e & \textrm{if}\; x \geq 0\; \textrm{or}\; e\in\mathbb{Z}, \\
 *     \textrm{undefined}, & \textrm{otherwise}.
 *     \end{cases}
 * \f]
 * and the signed power function, that is,
 * \f[
 *   x \mapsto \textrm{sign}(x) |x|^e
 * \f]
 * for some exponent \f$e\f$.
 *
 * @{
 */

/** creates a power expression */
SCIP_EXPORT
SCIP_RETCODE SCIPcreateExprPow(
   SCIP*                 scip,               /**< SCIP data structure */
   SCIP_EXPR**           expr,               /**< pointer where to store expression */
   SCIP_EXPR*            child,              /**< single child */
   SCIP_Real             exponent,           /**< exponent of the power expression */
   SCIP_DECL_EXPR_OWNERCREATE((*ownercreate)), /**< function to call to create ownerdata */
   void*                 ownercreatedata     /**< data to pass to ownercreate */
   );

/** creates a signpower expression */
SCIP_EXPORT
SCIP_RETCODE SCIPcreateExprSignpower(
   SCIP*                 scip,               /**< SCIP data structure */
   SCIP_EXPR**           expr,               /**< pointer where to store expression */
   SCIP_EXPR*            child,              /**< single child */
   SCIP_Real             exponent,           /**< exponent of the power expression */
   SCIP_DECL_EXPR_OWNERCREATE((*ownercreate)), /**< function to call to create ownerdata */
   void*                 ownercreatedata     /**< data to pass to ownercreate */
   );

/** indicates whether expression is of signpower-type */
SCIP_EXPORT
SCIP_Bool SCIPisExprSignpower(
   SCIP*                 scip,               /**< SCIP data structure */
   SCIP_EXPR*            expr                /**< expression */
   );

/** @}
  * @}
  */

/** creates the handler for power expression and includes it into SCIP
 *
 * @ingroup ExprhdlrIncludes
 */
SCIP_EXPORT
SCIP_RETCODE SCIPincludeExprhdlrPow(
   SCIP*                 scip                /**< SCIP data structure */
   );

/** creates the handler for signed power expression and includes it into SCIP
 *
 * @ingroup ExprhdlrIncludes
 */
SCIP_EXPORT
SCIP_RETCODE SCIPincludeExprhdlrSignpower(
   SCIP*                 scip                /**< SCIP data structure */
   );

/** computes coefficients of linearization of a square term in a reference point */
SCIP_EXPORT
void SCIPaddSquareLinearization(
   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 */
   );

/** computes coefficients of secant of a square term */
SCIP_EXPORT
void SCIPaddSquareSecant(
   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*            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 */
   );

/** Separation for roots with exponent in [0,1] */
SCIP_EXPORT
void SCIPestimateRoot(
   SCIP*                 scip,               /**< SCIP data structure */
   SCIP_Real             exponent,           /**< exponent */
   SCIP_Bool             overestimate,       /**< should the power be overestimated? */
   SCIP_Real             xlb,                /**< lower bound on x */
   SCIP_Real             xub,                /**< upper bound on x */
   SCIP_Real             xref,               /**< reference point (where to linearize) */
   SCIP_Real*            constant,           /**< buffer to store constant term of estimator */
   SCIP_Real*            slope,              /**< buffer to store slope of estimator */
   SCIP_Bool*            islocal,            /**< buffer to store whether estimator only locally valid, that is,
                                                  it depends on given bounds */
   SCIP_Bool*            success             /**< buffer to store whether estimator could be computed */
   );

#ifdef __cplusplus
}
#endif

#endif /* __SCIP_EXPR_POW_H__ */