Detailed Description

Constraint handler for absolute power constraints $\textrm{lhs} \leq \textrm{sign}(x+a) |x+a|^n + c z \leq \textrm{rhs}$ .

Author: Stefan Vigerske

This constraint handler handles constraints of the form

$\textrm{lhs} \leq \textrm{sign}(x+a) |x+a|^n + c z \leq \textrm{rhs}$

for $n > 1.0$ a rational number, $a$ and $c$ arbitrary, and $x$ and $z$ variables. Note that $x$ can have $-a$ in the interior of its domain.

Constraints are enforced by separation, domain propagation, and spatial branching.

Cuts that separate on the convex hull of the graph of $\textrm{sign}(x+a) |x+a|^n$ are generated as long as they separate the relaxation solution. Otherwise, spatial branching on $x$ is applied.

Further, domain propagation is implemented to propagate bound changes on $x$ onto $z$ , and vice versa, and repropagation is implemented to allow for conflict analysis. During presolve, a pairwise comparison of absolute power constraints may allow to fix or aggregate some variables. See also

: Stefan Vigerske
Decomposition of Multistage Stochastic Programs and a Constraint Integer Programming Approach to Mixed-Integer Nonlinear Programming
PhD Thesis, Humboldt-University Berlin, 2012, submitted.

Definition in file cons_abspower.h.

#include "scip/scip.h"

Go to the source code of this file.

Functions
SCIP_RETCODE	SCIPincludeConshdlrAbspower (SCIP *scip)

SCIP_RETCODE	SCIPcreateConsAbspower (SCIP scip, SCIP_CONS cons, const char name, SCIP_VAR x, SCIP_VAR z, SCIP_Real exponent, SCIP_Real xoffset, SCIP_Real zcoef, 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	SCIPcreateConsBasicAbspower (SCIP scip, SCIP_CONS cons, const char name, SCIP_VAR x, SCIP_VAR z, SCIP_Real exponent, SCIP_Real xoffset, SCIP_Real zcoef, SCIP_Real lhs, SCIP_Real rhs)

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

SCIP_VAR *	SCIPgetNonlinearVarAbspower (SCIP scip, SCIP_CONS cons)

SCIP_VAR *	SCIPgetLinearVarAbspower (SCIP scip, SCIP_CONS cons)

SCIP_Real	SCIPgetExponentAbspower (SCIP scip, SCIP_CONS cons)

SCIP_Real	SCIPgetOffsetAbspower (SCIP scip, SCIP_CONS cons)

SCIP_Real	SCIPgetCoefLinearAbspower (SCIP scip, SCIP_CONS cons)

SCIP_Real	SCIPgetLhsAbspower (SCIP scip, SCIP_CONS cons)

SCIP_Real	SCIPgetRhsAbspower (SCIP scip, SCIP_CONS cons)

SCIP_Real	SCIPgetViolationAbspower (SCIP scip, SCIP_CONS cons, SCIP_SOL *sol)

Function Documentation

SCIP_RETCODE SCIPincludeConshdlrAbspower ( SCIP * scip )

creates the handler for absolute power constraints and includes it in SCIP

Parameters

scip	SCIP data structure

SCIP_RETCODE SCIPcreateConsAbspower	(	SCIP *	scip,
		SCIP_CONS **	cons,
		const char *	name,
		SCIP_VAR *	x,
		SCIP_VAR *	z,
		SCIP_Real	exponent,
		SCIP_Real	xoffset,
		SCIP_Real	zcoef,
		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 absolute power constraint

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
x	nonlinear variable x in constraint
z	linear variable z in constraint
exponent	exponent n of \|x+offset\|^n term in constraint
xoffset	offset in \|x+offset\|^n term in constraint
zcoef	coefficient of z in constraint
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 SCIPcreateConsBasicAbspower	(	SCIP *	scip,
		SCIP_CONS **	cons,
		const char *	name,
		SCIP_VAR *	x,
		SCIP_VAR *	z,
		SCIP_Real	exponent,
		SCIP_Real	xoffset,
		SCIP_Real	zcoef,
		SCIP_Real	lhs,
		SCIP_Real	rhs
	)

creates and captures an absolute power constraint in its most basic version, i. e., all constraint flags are set to their basic value as explained for the method SCIPcreateConsAbspower(); all flags can be set via SCIPconsSetFLAGNAME-methods in scip.h

See also: SCIPcreateConsAbspower() 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
x	nonlinear variable x in constraint
z	linear variable z in constraint
exponent	exponent n of \|x+offset\|^n term in constraint
xoffset	offset in \|x+offset\|^n term in constraint
zcoef	coefficient of z in constraint
lhs	left hand side of constraint
rhs	right hand side of constraint

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

gets the absolute power constraint as a nonlinear row representation

Parameters

scip	SCIP data structure
cons	constraint
nlrow	a buffer where to store pointer to nonlinear row

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

gets nonlinear variable x in absolute power constraint

Parameters

scip	SCIP data structure
cons	absolute power constraint

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

gets linear variable z in absolute power constraint

Parameters

scip	SCIP data structure
cons	absolute power constraint

SCIP_Real SCIPgetExponentAbspower	(	SCIP *	scip,
		SCIP_CONS *	cons
	)

gets exponent in power term in absolute power constraint

Parameters

scip	SCIP data structure
cons	absolute power constraint

SCIP_Real SCIPgetOffsetAbspower	(	SCIP *	scip,
		SCIP_CONS *	cons
	)

gets offset in power term in absolute power constraint

Parameters

scip	SCIP data structure
cons	absolute power constraint

SCIP_Real SCIPgetCoefLinearAbspower	(	SCIP *	scip,
		SCIP_CONS *	cons
	)

gets coefficient of linear variable in absolute power constraint

Parameters

scip	SCIP data structure
cons	absolute power constraint

SCIP_Real SCIPgetLhsAbspower	(	SCIP *	scip,
		SCIP_CONS *	cons
	)

gets left hand side in absolute power constraint

Parameters

scip	SCIP data structure
cons	absolute power constraint

SCIP_Real SCIPgetRhsAbspower	(	SCIP *	scip,
		SCIP_CONS *	cons
	)

gets right hand side in absolute power constraint

Parameters

scip	SCIP data structure
cons	absolute power constraint

SCIP_Real SCIPgetViolationAbspower	(	SCIP *	scip,
		SCIP_CONS *	cons,
		SCIP_SOL *	sol
	)

gets the absolute violation of a absolute power constraint by a solution

Parameters

scip	SCIP data structure
cons	absolute power constraint
sol	LP solution

SCIP

Detailed Description

Functions

Function Documentation