Detailed Description

constraint handler for quadratic constraints $\textrm{lhs} \leq \sum_{i,j=1}^n a_{i,j} x_ix_j + \sum_{i=1}^n b_i x_i \leq \textrm{rhs}$

Author: Stefan Vigerske

This constraint handler handles constraints of the form

$\textrm{lhs} \leq \sum_{i,j=1}^n a_{i,j} x_ix_j + \sum_{i=1}^n b_i x_i \leq \textrm{rhs}$

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

For semidefinite matrices $A=(a_{i,j})_{i,j}$ , cuts based on linearization of $\langle x, Ax\rangle$ are implemented. For underestimating a non-convex term, McCormick underestimators and secants for univariate concave quadratic terms are implemented. If $\langle x, Ax\rangle$ is factorable (i.e., can be written as product of two linear functions), specialized separation techniques (e.g., lifted tangent inequalities) that take the constraint sides into account are applied.

Branching is performed for variables in nonconvex terms, if the relaxation solution cannot be separated. Further, domain propagation is applied.

During presolve, variable products which contain binary variables may be reformulated into linear constraints, thereby introducing new variables.

See also

: Timo Berthold and Stefan Heinz and Stefan Vigerske
Extending a CIP framework to solve MIQCPs
In: Jon Lee and Sven Leyffer (eds.), Mixed-integer nonlinear optimization: Algorithmic advances and applications, IMA volumes in Mathematics and its Applications, volume 154, 427-444, 2012.

: 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.

: Pietro Belotti and Andrew J. Miller and Mahdi Namazifar
Linear inequalities for bounded products of variables
SIAG/OPT Views-and-News 22:1, 1-8, 2011.

Definition in file cons_quadratic.h.

#include "scip/scip.h"
#include "scip/intervalarith.h"
#include "nlpi/type_nlpi.h"

Go to the source code of this file.

Macros
#define	SCIP_DECL_QUADCONSUPGD(x)

Typedefs
typedef struct SCIP_QuadVarEventData	SCIP_QUADVAREVENTDATA

typedef struct SCIP_QuadVarTerm	SCIP_QUADVARTERM

typedef struct SCIP_BilinTerm	SCIP_BILINTERM

Functions
SCIP_RETCODE	SCIPincludeConshdlrQuadratic (SCIP *scip)

SCIP_RETCODE	SCIPincludeQuadconsUpgrade (SCIP scip, SCIP_DECL_QUADCONSUPGD((quadconsupgd)), int priority, SCIP_Bool active, const char *conshdlrname)

SCIP_RETCODE	SCIPcreateConsQuadratic (SCIP scip, SCIP_CONS cons, const char name, int nlinvars, SCIP_VAR *linvars, SCIP_Real lincoefs, int nquadterms, SCIP_VAR quadvars1, SCIP_VAR quadvars2, SCIP_Real *quadcoeffs, 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_RETCODE	SCIPcreateConsBasicQuadratic (SCIP scip, SCIP_CONS cons, const char name, int nlinvars, SCIP_VAR *linvars, SCIP_Real lincoefs, int nquadterms, SCIP_VAR quadvars1, SCIP_VAR quadvars2, SCIP_Real *quadcoefs, SCIP_Real lhs, SCIP_Real rhs)

SCIP_RETCODE	SCIPcreateConsQuadratic2 (SCIP scip, SCIP_CONS cons, const char name, int nlinvars, SCIP_VAR *linvars, SCIP_Real lincoefs, int nquadvarterms, SCIP_QUADVARTERM quadvarterms, int nbilinterms, SCIP_BILINTERM bilinterms, 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_RETCODE	SCIPcreateConsBasicQuadratic2 (SCIP scip, SCIP_CONS cons, const char name, int nlinvars, SCIP_VAR *linvars, SCIP_Real lincoefs, int nquadvarterms, SCIP_QUADVARTERM quadvarterms, int nbilinterms, SCIP_BILINTERM bilinterms, SCIP_Real lhs, SCIP_Real rhs)

void	SCIPaddConstantQuadratic (SCIP scip, SCIP_CONS cons, SCIP_Real constant)

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

SCIP_RETCODE	SCIPaddQuadVarQuadratic (SCIP scip, SCIP_CONS cons, SCIP_VAR *var, SCIP_Real lincoef, SCIP_Real sqrcoef)

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

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

SCIP_RETCODE	SCIPaddBilinTermQuadratic (SCIP scip, SCIP_CONS cons, SCIP_VAR var1, SCIP_VAR var2, SCIP_Real coef)

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

int	SCIPgetNLinearVarsQuadratic (SCIP scip, SCIP_CONS cons)

SCIP_VAR **	SCIPgetLinearVarsQuadratic (SCIP scip, SCIP_CONS cons)

SCIP_Real *	SCIPgetCoefsLinearVarsQuadratic (SCIP scip, SCIP_CONS cons)

int	SCIPgetNQuadVarTermsQuadratic (SCIP scip, SCIP_CONS cons)

SCIP_QUADVARTERM *	SCIPgetQuadVarTermsQuadratic (SCIP scip, SCIP_CONS cons)

SCIP_RETCODE	SCIPsortQuadVarTermsQuadratic (SCIP scip, SCIP_CONS cons)

SCIP_RETCODE	SCIPfindQuadVarTermQuadratic (SCIP scip, SCIP_CONS cons, SCIP_VAR var, int pos)

int	SCIPgetNBilinTermsQuadratic (SCIP scip, SCIP_CONS cons)

SCIP_BILINTERM *	SCIPgetBilinTermsQuadratic (SCIP scip, SCIP_CONS cons)

SCIP_Real	SCIPgetLhsQuadratic (SCIP scip, SCIP_CONS cons)

SCIP_Real	SCIPgetRhsQuadratic (SCIP scip, SCIP_CONS cons)

SCIP_RETCODE	SCIPcheckCurvatureQuadratic (SCIP scip, SCIP_CONS cons)

SCIP_Bool	SCIPisConvexQuadratic (SCIP scip, SCIP_CONS cons)

SCIP_Bool	SCIPisConcaveQuadratic (SCIP scip, SCIP_CONS cons)

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

SCIP_Bool	SCIPisLinearLocalQuadratic (SCIP scip, SCIP_CONS cons)

SCIP_RETCODE	SCIPaddToNlpiProblemQuadratic (SCIP scip, SCIP_CONS cons, SCIP_NLPI nlpi, SCIP_NLPIPROBLEM nlpiprob, SCIP_HASHMAP *scipvar2nlpivar, SCIP_Bool names)

SCIP_RETCODE	SCIPchgLhsQuadratic (SCIP scip, SCIP_CONS cons, SCIP_Real lhs)

SCIP_RETCODE	SCIPchgRhsQuadratic (SCIP scip, SCIP_CONS cons, SCIP_Real rhs)

SCIP_RETCODE	SCIPgetFeasibilityQuadratic (SCIP scip, SCIP_CONS cons, SCIP_SOL sol, SCIP_Real feasibility)

SCIP_RETCODE	SCIPgetActivityQuadratic (SCIP scip, SCIP_CONS cons, SCIP_SOL sol, SCIP_Real activity)

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

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

SCIP_RETCODE	SCIPchgBilinCoefQuadratic (SCIP scip, SCIP_CONS cons, SCIP_VAR var1, SCIP_VAR var2, SCIP_Real coef)

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 refpoint, SCIP_Real lincoef, SCIP_Real linconstant, SCIP_Bool success)

void	SCIPaddBilinLinearization (SCIP scip, SCIP_Real bilincoef, SCIP_Real refpointx, SCIP_Real refpointy, SCIP_Real lincoefx, SCIP_Real lincoefy, SCIP_Real linconstant, SCIP_Bool *success)

void	SCIPaddBilinMcCormick (SCIP scip, SCIP_Real bilincoef, SCIP_Real lbx, SCIP_Real ubx, SCIP_Real refpointx, SCIP_Real lby, SCIP_Real uby, SCIP_Real refpointy, SCIP_Bool overestimate, SCIP_Real lincoefx, SCIP_Real lincoefy, SCIP_Real linconstant, SCIP_Bool *success)

Macro Definition Documentation

#define SCIP_DECL_QUADCONSUPGD ( x )

Value:

SCIP_RETCODE x (SCIP* scip, SCIP_CONS* cons, \
      int nbinlin, int nbinquad, int nintlin, int nintquad, int nimpllin, int nimplquad, int ncontlin, int ncontquad, \
      SCIP_Bool integral, int* nupgdconss, SCIP_CONS** upgdconss, int upgdconsssize, SCIP_PRESOLTIMING presoltiming)

upgrading method for quadratic constraints into more specific constraints

the method might upgrade a quadratic constraint into a set of quadratic 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 quadratic constraint to upgrade
nbinlin : number of binary variables in linear part
nbinquad : number of binary variables in quadratic part
nintlin : number of integer variables in linear part
nintquad : number of integer variables in quadratic part
nimpllin : number of implicit integer variables in linear part
nimplquad : number of implicit integer variables in quadratic part
ncontlin : number of continuous variables in linear part
ncontquad : number of continuous variables in quadratic part
integral : TRUE iff constraints activity value is always integral
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
presoltiming : current presolve timing

Definition at line 129 of file cons_quadratic.h.

Typedef Documentation

typedef struct SCIP_QuadVarEventData SCIP_QUADVAREVENTDATA

event data for variable bound changes in quadratic constraints

Definition at line 71 of file cons_quadratic.h.

typedef struct SCIP_QuadVarTerm SCIP_QUADVARTERM

Definition at line 87 of file cons_quadratic.h.

typedef struct SCIP_BilinTerm SCIP_BILINTERM

Definition at line 98 of file cons_quadratic.h.

Function Documentation

SCIP_RETCODE SCIPincludeConshdlrQuadratic ( SCIP * scip )

creates the handler for quadratic constraints and includes it in SCIP

Parameters

scip	SCIP data structure

SCIP_RETCODE SCIPincludeQuadconsUpgrade	(	SCIP *	scip,
		SCIP_DECL_QUADCONSUPGD((*quadconsupgd))	,
		int	priority,
		SCIP_Bool	active,
		const char *	conshdlrname
	)

includes a quadratic constraint upgrade method into the quadratic constraint handler

Parameters

scip	SCIP data structure
priority	priority of upgrading method
active	should the upgrading method be active by default?
conshdlrname	name of the constraint handler

SCIP_RETCODE SCIPcreateConsQuadratic	(	SCIP *	scip,
		SCIP_CONS **	cons,
		const char *	name,
		int	nlinvars,
		SCIP_VAR **	linvars,
		SCIP_Real *	lincoefs,
		int	nquadterms,
		SCIP_VAR **	quadvars1,
		SCIP_VAR **	quadvars2,
		SCIP_Real *	quadcoeffs,
		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
	)

Creates and captures a quadratic constraint.

The constraint should be given in the form

$\ell \leq \sum_{i=1}^n b_i x_i + \sum_{j=1}^m a_j y_j z_j \leq u,$

where $x_i = y_j = z_k$ is possible.

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 terms (n)
linvars	variables in linear part (x_i) or NULL if nlinvars == 0
lincoefs	coefficients of variables in linear part (b_i) or NULL if nlinvars == 0
nquadterms	number of quadratic terms (m)
quadvars1	array with first variables in quadratic terms (y_j) or NULL if nquadterms == 0
quadvars2	array with second variables in quadratic terms (z_j) or NULL if nquadterms == 0
quadcoeffs	array with coefficients of quadratic terms (a_j) or NULL if nquadterms == 0
lhs	left hand side of quadratic equation (l)
rhs	right hand side of quadratic equation (u)
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 separated 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'.

SCIP_RETCODE SCIPcreateConsBasicQuadratic	(	SCIP *	scip,
		SCIP_CONS **	cons,
		const char *	name,
		int	nlinvars,
		SCIP_VAR **	linvars,
		SCIP_Real *	lincoefs,
		int	nquadterms,
		SCIP_VAR **	quadvars1,
		SCIP_VAR **	quadvars2,
		SCIP_Real *	quadcoefs,
		SCIP_Real	lhs,
		SCIP_Real	rhs
	)

creates and captures a quadratic constraint in its most basic variant, i. e., with all constraint flags set to their default values, which can be set afterwards using SCIPsetConsFLAGNAME() in scip.h

The constraint should be given in the form

$\ell \leq \sum_{i=1}^n b_i x_i + \sum_{j=1}^m a_j y_jz_j \leq u,$

where $x_i = y_j = z_k$ is possible.

See Also: SCIPcreateConsQuadratic() for the default 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 terms (n)
linvars	array with variables in linear part (x_i)
lincoefs	array with coefficients of variables in linear part (b_i)
nquadterms	number of quadratic terms (m)
quadvars1	array with first variables in quadratic terms (y_j)
quadvars2	array with second variables in quadratic terms (z_j)
quadcoefs	array with coefficients of quadratic terms (a_j)
lhs	left hand side of quadratic equation (ell)
rhs	right hand side of quadratic equation (u)

SCIP_RETCODE SCIPcreateConsQuadratic2	(	SCIP *	scip,
		SCIP_CONS **	cons,
		const char *	name,
		int	nlinvars,
		SCIP_VAR **	linvars,
		SCIP_Real *	lincoefs,
		int	nquadvarterms,
		SCIP_QUADVARTERM *	quadvarterms,
		int	nbilinterms,
		SCIP_BILINTERM *	bilinterms,
		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
	)

creates and captures a quadratic constraint.

The constraint should be given in the form

$\ell \leq \sum_{i=1}^n b_i x_i + \sum_{j=1}^m (a_j y_j^2 + b_j y_j) + \sum_{k=1}^p c_k v_k w_k \leq u.$

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 terms (n)
linvars	array with variables in linear part (x_i)
lincoefs	array with coefficients of variables in linear part (b_i)
nquadvarterms	number of quadratic terms (m)
quadvarterms	quadratic variable terms
nbilinterms	number of bilinear terms (p)
bilinterms	bilinear terms
lhs	constraint left hand side (ell)
rhs	constraint right hand side (u)
initial	should the LP relaxation of constraint be in the initial LP?
separate	should the constraint be separated during LP processing?
enforce	should the constraint be enforced during node processing?
check	should the constraint be checked for feasibility?
propagate	should the constraint be propagated during node processing?
local	is constraint only valid locally?
modifiable	is constraint modifiable (subject to column generation)?
dynamic	is constraint dynamic?
removable	should the constraint be removed from the LP due to aging or cleanup?

SCIP_RETCODE SCIPcreateConsBasicQuadratic2	(	SCIP *	scip,
		SCIP_CONS **	cons,
		const char *	name,
		int	nlinvars,
		SCIP_VAR **	linvars,
		SCIP_Real *	lincoefs,
		int	nquadvarterms,
		SCIP_QUADVARTERM *	quadvarterms,
		int	nbilinterms,
		SCIP_BILINTERM *	bilinterms,
		SCIP_Real	lhs,
		SCIP_Real	rhs
	)

creates and captures a quadratic constraint in its most basic variant, i. e., with all constraint flags set to their default values, which can be set afterwards using SCIPsetConsFLAGNAME() in scip.h

The constraint should be given in the form

$\ell \leq \sum_{i=1}^n b_i x_i + \sum_{j=1}^m (a_j y_j^2 + b_j y_j) + \sum_{k=1}^p c_kv_kw_k \leq u.$

See Also: SCIPcreateConsQuadratic2() for the default 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 terms (n)
linvars	array with variables in linear part (x_i)
lincoefs	array with coefficients of variables in linear part (b_i)
nquadvarterms	number of quadratic terms (m)
quadvarterms	quadratic variable terms
nbilinterms	number of bilinear terms (p)
bilinterms	bilinear terms
lhs	constraint left hand side (ell)
rhs	constraint right hand side (u)

void SCIPaddConstantQuadratic	(	SCIP *	scip,
		SCIP_CONS *	cons,
		SCIP_Real	constant
	)

Adds a constant to the constraint function, that is, subtracts a constant from both sides

Parameters

scip	SCIP data structure
cons	constraint
constant	constant to subtract from both sides

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

Adds a linear variable with coefficient to a quadratic constraint.

Parameters

scip	SCIP data structure
cons	constraint
var	variable
coef	coefficient of variable

SCIP_RETCODE SCIPaddQuadVarQuadratic	(	SCIP *	scip,
		SCIP_CONS *	cons,
		SCIP_VAR *	var,
		SCIP_Real	lincoef,
		SCIP_Real	sqrcoef
	)

Adds a quadratic variable with linear and square coefficient to a quadratic constraint.

Parameters

scip	SCIP data structure
cons	constraint
var	variable
lincoef	linear coefficient of variable
sqrcoef	square coefficient of variable

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

Adds a linear coefficient for a quadratic variable.

Variable will be added with square coefficient 0.0 if not existing yet.

Parameters

scip	SCIP data structure
cons	constraint
var	variable
coef	value to add to linear coefficient of variable

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

Adds a square coefficient for a quadratic variable.

Variable will be added with linear coefficient 0.0 if not existing yet.

Parameters

scip	SCIP data structure
cons	constraint
var	variable
coef	value to add to square coefficient of variable

SCIP_RETCODE SCIPaddBilinTermQuadratic	(	SCIP *	scip,
		SCIP_CONS *	cons,
		SCIP_VAR *	var1,
		SCIP_VAR *	var2,
		SCIP_Real	coef
	)

Adds a bilinear term to a quadratic constraint.

Variables will be added with linear and square coefficient 0.0 if not existing yet. If variables are equal, only the square coefficient of the variable is updated.

Parameters

scip	SCIP data structure
cons	constraint
var1	first variable
var2	second variable
coef	coefficient of bilinear term

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

Gets the quadratic constraint as a nonlinear row representation.

Parameters

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

int SCIPgetNLinearVarsQuadratic	(	SCIP *	scip,
		SCIP_CONS *	cons
	)

Gets the number of variables in the linear part of a quadratic constraint.

Parameters

scip	SCIP data structure
cons	constraint

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

Gets the variables in the linear part of a quadratic constraint. Length is given by SCIPgetNLinearVarsQuadratic.

Parameters

scip	SCIP data structure
cons	constraint

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

Gets the coefficients in the linear part of a quadratic constraint. Length is given by SCIPgetNQuadVarsQuadratic.

Parameters

scip	SCIP data structure
cons	constraint

int SCIPgetNQuadVarTermsQuadratic	(	SCIP *	scip,
		SCIP_CONS *	cons
	)

Gets the number of quadratic variable terms of a quadratic constraint.

Parameters

scip	SCIP data structure
cons	constraint

SCIP_QUADVARTERM* SCIPgetQuadVarTermsQuadratic	(	SCIP *	scip,
		SCIP_CONS *	cons
	)

Gets the quadratic variable terms of a quadratic constraint. Length is given by SCIPgetNQuadVarTermsQuadratic.

Parameters

scip	SCIP data structure
cons	constraint

SCIP_RETCODE SCIPsortQuadVarTermsQuadratic	(	SCIP *	scip,
		SCIP_CONS *	cons
	)

Ensures that quadratic variable terms are sorted.

Parameters

scip	SCIP data structure
cons	constraint

SCIP_RETCODE SCIPfindQuadVarTermQuadratic	(	SCIP *	scip,
		SCIP_CONS *	cons,
		SCIP_VAR *	var,
		int *	pos
	)

Finds the position of a quadratic variable term for a given variable.

Note: If the quadratic variable terms have not been sorted before, then a search may reorder the current order of the terms.

Parameters

scip	SCIP data structure
cons	constraint
var	variable to search for
pos	buffer to store position of quadvarterm for var, or -1 if not found

int SCIPgetNBilinTermsQuadratic	(	SCIP *	scip,
		SCIP_CONS *	cons
	)

Gets the number of bilinear terms of a quadratic constraint.

Parameters

scip	SCIP data structure
cons	constraint

SCIP_BILINTERM* SCIPgetBilinTermsQuadratic	(	SCIP *	scip,
		SCIP_CONS *	cons
	)

Gets the bilinear terms of a quadratic constraint. Length is given by SCIPgetNBilinTermQuadratic.

Parameters

scip	SCIP data structure
cons	constraint

SCIP_Real SCIPgetLhsQuadratic	(	SCIP *	scip,
		SCIP_CONS *	cons
	)

Gets the left hand side of a quadratic constraint.

Parameters

scip	SCIP data structure
cons	constraint

SCIP_Real SCIPgetRhsQuadratic	(	SCIP *	scip,
		SCIP_CONS *	cons
	)

Gets the right hand side of a quadratic constraint.

Parameters

scip	SCIP data structure
cons	constraint

SCIP_RETCODE SCIPcheckCurvatureQuadratic	(	SCIP *	scip,
		SCIP_CONS *	cons
	)

Check the quadratic function of a quadratic constraint for its semi-definiteness, if not done yet.

Parameters

scip	SCIP data structure
cons	constraint

SCIP_Bool SCIPisConvexQuadratic	(	SCIP *	scip,
		SCIP_CONS *	cons
	)

Indicates whether the quadratic function of a quadratic constraint is (known to be) convex.

Parameters

scip	SCIP data structure
cons	constraint

SCIP_Bool SCIPisConcaveQuadratic	(	SCIP *	scip,
		SCIP_CONS *	cons
	)

Indicates whether the quadratic function of a quadratic constraint is (known to be) concave.

Parameters

scip	SCIP data structure
cons	constraint

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

Gets the violation of a 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

SCIP_Bool SCIPisLinearLocalQuadratic	(	SCIP *	scip,
		SCIP_CONS *	cons
	)

Indicates whether the quadratic constraint is local w.r.t. the current local bounds.

That is, checks whether each variable with a square term is fixed and for each bilinear term at least one variable is fixed.

Parameters

scip	SCIP data structure
cons	constraint

SCIP_RETCODE SCIPaddToNlpiProblemQuadratic	(	SCIP *	scip,
		SCIP_CONS *	cons,
		SCIP_NLPI *	nlpi,
		SCIP_NLPIPROBLEM *	nlpiprob,
		SCIP_HASHMAP *	scipvar2nlpivar,
		SCIP_Bool	names
	)

Adds the constraint to an NLPI problem.

Parameters

scip	SCIP data structure
cons	constraint
nlpi	interface to NLP solver
nlpiprob	NLPI problem where to add constraint
scipvar2nlpivar	mapping from SCIP variables to variable indices in NLPI
names	whether to pass constraint names to NLPI

SCIP_RETCODE SCIPchgLhsQuadratic	(	SCIP *	scip,
		SCIP_CONS *	cons,
		SCIP_Real	lhs
	)

sets the left hand side of a quadratic constraint

Note: This method may only be called during problem creation stage for an original constraint.

Parameters

scip	SCIP data structure
cons	constraint data
lhs	new left hand side

SCIP_RETCODE SCIPchgRhsQuadratic	(	SCIP *	scip,
		SCIP_CONS *	cons,
		SCIP_Real	rhs
	)

sets the right hand side of a quadratic constraint

Note: This method may only be called during problem creation stage for an original constraint.

Parameters

scip	SCIP data structure
cons	constraint data
rhs	new right hand side

SCIP_RETCODE SCIPgetFeasibilityQuadratic	(	SCIP *	scip,
		SCIP_CONS *	cons,
		SCIP_SOL *	sol,
		SCIP_Real *	feasibility
	)

gets the feasibility of the quadratic constraint in the given solution gets the feasibility of the quadratic constraint in the given solution

Parameters

scip	SCIP data structure
cons	constraint data
sol	solution, or NULL to use current node's solution
feasibility	pointer to store the feasibility

SCIP_RETCODE SCIPgetActivityQuadratic	(	SCIP *	scip,
		SCIP_CONS *	cons,
		SCIP_SOL *	sol,
		SCIP_Real *	activity
	)

gets the activity of the quadratic constraint in the given solution

Parameters

scip	SCIP data structure
cons	constraint data
sol	solution, or NULL to use current node's solution
activity	pointer to store the activity

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

changes the linear coefficient value for a given quadratic variable in a quadratic constraint data; if not available, it adds it

Note: this is only allowed for original constraints and variables in problem creation stage

Parameters

scip	SCIP data structure
cons	constraint data
var	quadratic variable
coef	new coefficient

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

changes the square coefficient value for a given quadratic variable in a quadratic constraint data; if not available, it adds it

Note: this is only allowed for original constraints and variables in problem creation stage

Parameters

scip	SCIP data structure
cons	constraint data
var	quadratic variable
coef	new coefficient

SCIP_RETCODE SCIPchgBilinCoefQuadratic	(	SCIP *	scip,
		SCIP_CONS *	cons,
		SCIP_VAR *	var1,
		SCIP_VAR *	var2,
		SCIP_Real	coef
	)

changes the bilinear coefficient value for a given quadratic variable in a quadratic constraint data; if not available, it adds it

Note: this is only allowed for original constraints and variables in problem creation stage

Parameters

scip	SCIP data structure
cons	constraint
var1	first quadratic variable
var2	second quadratic variable
coef	coefficient of bilinear term

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

void SCIPaddSquareSecant	(	SCIP *	scip,
		SCIP_Real	sqrcoef,
		SCIP_Real	lb,
		SCIP_Real	ub,
		SCIP_Real	refpoint,
		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
refpoint	point for which to compute value of linearization
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

void SCIPaddBilinLinearization	(	SCIP *	scip,
		SCIP_Real	bilincoef,
		SCIP_Real	refpointx,
		SCIP_Real	refpointy,
		SCIP_Real *	lincoefx,
		SCIP_Real *	lincoefy,
		SCIP_Real *	linconstant,
		SCIP_Bool *	success
	)

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

Parameters

scip	SCIP data structure
bilincoef	coefficient of bilinear term
refpointx	point where to linearize first variable
refpointy	point where to linearize second variable
lincoefx	buffer to add coefficient of first variable in linearization
lincoefy	buffer to add coefficient of second variable in linearization
linconstant	buffer to add constant of linearization
success	buffer to set to FALSE if linearization has failed due to large numbers

void SCIPaddBilinMcCormick	(	SCIP *	scip,
		SCIP_Real	bilincoef,
		SCIP_Real	lbx,
		SCIP_Real	ubx,
		SCIP_Real	refpointx,
		SCIP_Real	lby,
		SCIP_Real	uby,
		SCIP_Real	refpointy,
		SCIP_Bool	overestimate,
		SCIP_Real *	lincoefx,
		SCIP_Real *	lincoefy,
		SCIP_Real *	linconstant,
		SCIP_Bool *	success
	)

computes coefficients of McCormick under- or overestimation of a bilinear term

Parameters

scip	SCIP data structure
bilincoef	coefficient of bilinear term
lbx	lower bound on first variable
ubx	upper bound on first variable
refpointx	reference point for first variable
lby	lower bound on second variable
uby	upper bound on second variable
refpointy	reference point for second variable
overestimate	whether to compute an overestimator instead of an underestimator
lincoefx	buffer to add coefficient of first variable in linearization
lincoefy	buffer to add coefficient of second variable in linearization
linconstant	buffer to add constant of linearization
success	buffer to set to FALSE if linearization has failed due to large numbers

SCIP

Detailed Description

Macros

Typedefs

Functions

Macro Definition Documentation

Typedef Documentation

Function Documentation