Detailed Description

constraint handler for bivariate nonlinear constraints $\textrm{lhs} \leq f(x,y) + c z \leq \textrm{rhs}$

Author: Martin Ballerstein; Dennis Michaels; Stefan Vigerske

This constraint handler handles constraints of the form

$\textrm{lhs} \leq f(x,y) + c z \leq \textrm{rhs}$

for a bivariate nonlinear function $f(x,y)$ (given as expression tree) that has a fixed convexity behaviour, that is, has to be either jointly convex in $(x,y)$ , or convex in $x$ and concave in $y$ , or convex in $x$ and convex in $y$ , but indefinite w.r.t. $(x,y)$ . See also

: Martin Ballerstein, Dennis Michaels, and Stefan Vigerske
Linear Underestimators for bivariate functions with a fixed convexity behavior
ZIB Report 13-02, 2013. http://opus4.kobv.de/opus4-zib/frontdoor/index/index/docId/1764

Definition in file cons_bivariate.h.

#include "scip/scip.h"

Go to the source code of this file.

Enumerations
enum	SCIP_BIVAR_CONVEXITY { SCIP_BIVAR_ALLCONVEX = 0, SCIP_BIVAR_1CONVEX_INDEFINITE = 1, SCIP_BIVAR_CONVEX_CONCAVE = 2, SCIP_BIVAR_UNKNOWN = 3 }

Functions
SCIP_RETCODE	SCIPincludeConshdlrBivariate (SCIP *scip)

SCIP_RETCODE	SCIPcreateConsBivariate (SCIP scip, SCIP_CONS cons, const char name, SCIP_EXPRTREE f, SCIP_BIVAR_CONVEXITY convextype, SCIP_VAR z, 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	SCIPcreateConsBasicBivariate (SCIP scip, SCIP_CONS cons, const char name, SCIP_EXPRTREE f, SCIP_BIVAR_CONVEXITY convextype, SCIP_VAR z, SCIP_Real zcoef, SCIP_Real lhs, SCIP_Real rhs)

SCIP_VAR *	SCIPgetLinearVarBivariate (SCIP scip, SCIP_CONS cons)

SCIP_Real	SCIPgetLinearCoefBivariate (SCIP scip, SCIP_CONS cons)

SCIP_EXPRTREE *	SCIPgetExprtreeBivariate (SCIP scip, SCIP_CONS cons)

SCIP_Real	SCIPgetLhsBivariate (SCIP scip, SCIP_CONS cons)

SCIP_Real	SCIPgetRhsBivariate (SCIP scip, SCIP_CONS cons)

Enumeration Type Documentation

enum SCIP_BIVAR_CONVEXITY

Enumerator
SCIP_BIVAR_ALLCONVEX
SCIP_BIVAR_1CONVEX_INDEFINITE
SCIP_BIVAR_CONVEX_CONCAVE
SCIP_BIVAR_UNKNOWN

Definition at line 50 of file cons_bivariate.h.

Function Documentation

SCIP_RETCODE SCIPincludeConshdlrBivariate ( SCIP * scip )

creates the handler for bivariate constraints and includes it in SCIP

Parameters

scip	SCIP data structure

SCIP_RETCODE SCIPcreateConsBivariate	(	SCIP *	scip,
		SCIP_CONS **	cons,
		const char *	name,
		SCIP_EXPRTREE *	f,
		SCIP_BIVAR_CONVEXITY	convextype,
		SCIP_VAR *	z,
		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 bivariate 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
f	expression tree specifying bivariate function f(x,y)
convextype	kind of convexity of f(x,y)
z	linear variable in constraint
zcoef	coefficient of linear variable
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 SCIPcreateConsBasicBivariate	(	SCIP *	scip,
		SCIP_CONS **	cons,
		const char *	name,
		SCIP_EXPRTREE *	f,
		SCIP_BIVAR_CONVEXITY	convextype,
		SCIP_VAR *	z,
		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 SCIPcreateConsBivariate(); all flags can be set via SCIPconsSetFLAGNAME-methods in cons.h

See Also: SCIPcreateConsBivariate() 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
f	expression tree specifying bivariate function f(x,y)
convextype	kind of convexity of f(x,y)
z	linear variable in constraint
zcoef	coefficient of linear variable
lhs	left hand side of constraint
rhs	right hand side of constraint

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

gets the linear variable of a bivariate constraint, or NULL if no such variable

Parameters

scip	SCIP data structure
cons	constraint

SCIP_Real SCIPgetLinearCoefBivariate	(	SCIP *	scip,
		SCIP_CONS *	cons
	)

gets the coefficients of the linear variable of a bivariate constraint

Parameters

scip	SCIP data structure
cons	constraint

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

gets the expression tree of a bivariate constraint

Parameters

scip	SCIP data structure
cons	constraint

SCIP_Real SCIPgetLhsBivariate	(	SCIP *	scip,
		SCIP_CONS *	cons
	)

gets the left hand side of a bivariate constraint

Parameters

scip	SCIP data structure
cons	constraint

SCIP_Real SCIPgetRhsBivariate	(	SCIP *	scip,
		SCIP_CONS *	cons
	)

gets the right hand side of a bivariate constraint

Parameters

scip	SCIP data structure
cons	constraint

SCIP

Detailed Description

Enumerations

Functions

Enumeration Type Documentation

Function Documentation