Detailed Description

power and signed power expression handlers

Author: Benjamin Mueller

Definition in file expr_pow.h.

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

Functions
SCIP_RETCODE	SCIPincludeExprhdlrPow (SCIP *scip)

SCIP_RETCODE	SCIPincludeExprhdlrSignpower (SCIP *scip)

void	SCIPaddSquareLinearization (SCIP scip, SCIP_Real sqrcoef, SCIP_Real refpoint, SCIP_Bool isint, SCIP_Real lincoef, SCIP_Real linconstant, SCIP_Bool success)

void	SCIPaddSquareSecant (SCIP scip, SCIP_Real sqrcoef, SCIP_Real lb, SCIP_Real ub, SCIP_Real lincoef, SCIP_Real linconstant, SCIP_Bool success)

void	SCIPestimateRoot (SCIP scip, SCIP_Real exponent, SCIP_Bool overestimate, SCIP_Real xlb, SCIP_Real xub, SCIP_Real xref, SCIP_Real constant, SCIP_Real slope, SCIP_Bool islocal, SCIP_Bool *success)

Power and signed power expression
These expression handlers provide the power function, that is, \[ x \mapsto \begin{cases} x^e & \textrm{if}\; x \geq 0\; \textrm{or}\; e\in\mathbb{Z}, \\ \textrm{undefined}, & \textrm{otherwise}. \end{cases} \] and the signed power function, that is, \[ x \mapsto \textrm{sign}(x) \|x\|^e \] for some exponent \(e\).
SCIP_RETCODE	SCIPcreateExprPow (SCIP scip, SCIP_EXPR expr, SCIP_EXPR child, SCIP_Real exponent, SCIP_DECL_EXPR_OWNERCREATE((ownercreate)), void ownercreatedata)

SCIP_RETCODE	SCIPcreateExprSignpower (SCIP scip, SCIP_EXPR expr, SCIP_EXPR child, SCIP_Real exponent, SCIP_DECL_EXPR_OWNERCREATE((ownercreate)), void ownercreatedata)

SCIP_Bool	SCIPisExprSignpower (SCIP scip, SCIP_EXPR expr)

Function Documentation

◆ SCIPaddSquareLinearization()

void SCIPaddSquareLinearization	(	SCIP *	scip,
		SCIP_Real	sqrcoef,
		SCIP_Real	refpoint,
		SCIP_Bool	isint,
		SCIP_Real *	lincoef,
		SCIP_Real *	linconstant,
		SCIP_Bool *	success
	)

computes coefficients of linearization of a square term in a reference point

Parameters

scip	SCIP data structure
sqrcoef	coefficient of square term
refpoint	point where to linearize
isint	whether corresponding variable is a discrete variable, and thus linearization could be moved
lincoef	buffer to add coefficient of linearization
linconstant	buffer to add constant of linearization
success	buffer to set to FALSE if linearization has failed due to large numbers

Definition at line 3254 of file expr_pow.c.

References FALSE, NULL, REALABS, SCIP_Real, SCIPaddSquareSecant(), SCIPfloor(), SCIPisInfinity(), and SCIPisIntegral().

Referenced by addBilinearTermToCut(), addRltTerm(), buildPowEstimator(), and SCIPisExprSignpower().

◆ SCIPaddSquareSecant()

void SCIPaddSquareSecant	(	SCIP *	scip,
		SCIP_Real	sqrcoef,
		SCIP_Real	lb,
		SCIP_Real	ub,
		SCIP_Real *	lincoef,
		SCIP_Real *	linconstant,
		SCIP_Bool *	success
	)

computes coefficients of secant of a square term

Parameters

scip	SCIP data structure
sqrcoef	coefficient of square term
lb	lower bound on variable
ub	upper bound on variable
lincoef	buffer to add coefficient of secant
linconstant	buffer to add constant of secant
success	buffer to set to FALSE if secant has failed due to large numbers or unboundedness

Definition at line 3322 of file expr_pow.c.

References FALSE, NULL, REALABS, SCIP_Real, SCIPestimateRoot(), SCIPisInfinity(), and SCIPisLE().

Referenced by addBilinearTermToCut(), addRltTerm(), buildPowEstimator(), and SCIPaddSquareLinearization().

◆ SCIPestimateRoot()

void SCIPestimateRoot	(	SCIP *	scip,
		SCIP_Real	exponent,
		SCIP_Bool	overestimate,
		SCIP_Real	xlb,
		SCIP_Real	xub,
		SCIP_Real	xref,
		SCIP_Real *	constant,
		SCIP_Real *	slope,
		SCIP_Bool *	islocal,
		SCIP_Bool *	success
	)

Separation for roots with exponent in [0,1]

x^0.5 with x >= 0

 8 +-------------------------------------------------------------------—+
   |             +             +              +             +             |
 7 |-+                                                     x**0.5 ********|
   |                                                             *********|
   |                                                      ********        |
 6 |-+                                             ********             +-|
   |                                         ******                       |
 5 |-+                                 ******                           +-|
   |                             ******                                   |
   |                        *****                                         |
 4 |-+                  ****                                            +-|
   |               *****                                                  |
 3 |-+          ****                                                    +-|
   |         ***                                                          |
   |      ***                                                             |
 2 |-+  **                                                              +-|
   |  **                                                                  |
 1 |**                                                                  +-|
   |*                                                                     |
   |*            +             +              +             +             |
 0 +-------------------------------------------------------------------—+
   0             10            20             30            40            50

Parameters

scip	SCIP data structure
exponent	exponent
overestimate	should the power be overestimated?
xlb	lower bound on x
xub	upper bound on x
xref	reference point (where to linearize)
constant	buffer to store constant term of estimator
slope	buffer to store slope of estimator
islocal	buffer to store whether estimator only locally valid, that is, it depends on given bounds
success	buffer to store whether estimator could be computed

Definition at line 3396 of file expr_pow.c.

References computeSecant(), computeTangent(), FALSE, NULL, SCIP_Real, SCIPgetExponentExprPow(), SCIPisZero(), and TRUE.

Referenced by buildPowEstimator(), and SCIPaddSquareSecant().

SCIP

Detailed Description

Functions

Function Documentation

◆ SCIPaddSquareLinearization()

◆ SCIPaddSquareSecant()

◆ SCIPestimateRoot()