Nonlinear Data

Detailed Description

methods for nonlinear data

Functions
SCIP_EXPORT void	SCIPaddSquareLinearization (SCIP *scip, SCIP_Real sqrcoef, SCIP_Real refpoint, SCIP_Bool isint, SCIP_Real *lincoef, SCIP_Real *linconstant, SCIP_Bool *success)
SCIP_EXPORT 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)
SCIP_EXPORT 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)
SCIP_EXPORT 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)
SCIP_EXPORT void	SCIPcomputeBilinEnvelope1 (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 xcoef, SCIP_Real ycoef, SCIP_Real constant, SCIP_Real *RESTRICT lincoefx, SCIP_Real *RESTRICT lincoefy, SCIP_Real *RESTRICT linconstant, SCIP_Bool *RESTRICT success)
SCIP_EXPORT void	SCIPcomputeBilinEnvelope2 (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 alpha1, SCIP_Real beta1, SCIP_Real gamma1, SCIP_Real alpha2, SCIP_Real beta2, SCIP_Real gamma2, SCIP_Real *RESTRICT lincoefx, SCIP_Real *RESTRICT lincoefy, SCIP_Real *RESTRICT linconstant, SCIP_Bool *RESTRICT success)
SCIP_EXPORT SCIP_RETCODE	SCIPcreateNlpiProb (SCIP *scip, SCIP_NLPI *nlpi, SCIP_NLROW **nlrows, int nnlrows, SCIP_NLPIPROBLEM *nlpiprob, SCIP_HASHMAP *var2idx, SCIP_Real *nlscore, SCIP_Real cutoffbound, SCIP_Bool setobj, SCIP_Bool onlyconvex)
SCIP_EXPORT SCIP_RETCODE	SCIPupdateNlpiProb (SCIP *scip, SCIP_NLPI *nlpi, SCIP_NLPIPROBLEM *nlpiprob, SCIP_HASHMAP *var2nlpiidx, SCIP_VAR **nlpivars, int nlpinvars, SCIP_Real cutoffbound)
SCIP_EXPORT SCIP_RETCODE	SCIPaddNlpiProbRows (SCIP *scip, SCIP_NLPI *nlpi, SCIP_NLPIPROBLEM *nlpiprob, SCIP_HASHMAP *var2idx, SCIP_ROW **rows, int nrows)

Function Documentation

SCIPaddSquareLinearization()

SCIP_EXPORT 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 52 of file scip_nonlinear.c.

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

Referenced by addBilinearTermToCut(), generateCutConvex(), and generateCutNonConvex().

SCIPaddSquareSecant()

SCIP_EXPORT 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

Definition at line 120 of file scip_nonlinear.c.

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

Referenced by addBilinearTermToCut(), and generateCutNonConvex().

SCIPaddBilinLinearization()

SCIP_EXPORT 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

Definition at line 170 of file scip_nonlinear.c.

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

Referenced by generateCutConvex().

SCIPaddBilinMcCormick()

SCIP_EXPORT 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

Definition at line 217 of file scip_nonlinear.c.

References FALSE, MAX, MIN, NULL, REALABS, SCIP_Real, SCIPdebugMsg, SCIPisGE(), SCIPisInfinity(), SCIPisLE(), and SCIPisRelEQ().

Referenced by addBilinearTermToCut(), and generateCutNonConvex().

SCIPcomputeBilinEnvelope1()

SCIP_EXPORT void SCIPcomputeBilinEnvelope1	(	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	xcoef,
		SCIP_Real	ycoef,
		SCIP_Real	constant,
		SCIP_Real *RESTRICT	lincoefx,
		SCIP_Real *RESTRICT	lincoefy,
		SCIP_Real *RESTRICT	linconstant,
		SCIP_Bool *RESTRICT	success
	)

computes coefficients of linearization of a bilinear term in a reference point when given a linear inequality involving only the variables of the bilinear term

Note

the formulas are extracted from "Convex envelopes of bivariate functions through the solution of KKT systems" by Marco Locatelli

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
xcoef	x coefficient of linear inequality; must be in {-1,0,1}
ycoef	y coefficient of linear inequality
constant	constant of linear inequality
lincoefx	buffer to store coefficient of first variable in linearization
lincoefy	buffer to store coefficient of second variable in linearization
linconstant	buffer to store constant of linearization
success	buffer to store whether linearization was successful

Definition at line 426 of file scip_nonlinear.c.

References FALSE, NULL, QUAD, QUAD_SCALE, QUAD_TO_DBL, SCIP_INVALID, SCIP_Real, SCIPisFeasEQ(), SCIPisFeasGE(), SCIPisFeasGT(), SCIPisFeasLE(), SCIPisGE(), SCIPisInfinity(), SCIPisLE(), SCIPisNegative(), SCIPisZero(), SCIPquadprecDivDD, SCIPquadprecDivQQ, SCIPquadprecProdDD, SCIPquadprecProdQD, SCIPquadprecProdQQ, SCIPquadprecSquareQ, SCIPquadprecSumDD, SCIPquadprecSumQD, and SCIPquadprecSumQQ.

Referenced by updateBilinearRelaxation().

SCIPcomputeBilinEnvelope2()

SCIP_EXPORT void SCIPcomputeBilinEnvelope2	(	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	xcoef1,
		SCIP_Real	ycoef1,
		SCIP_Real	constant1,
		SCIP_Real	xcoef2,
		SCIP_Real	ycoef2,
		SCIP_Real	constant2,
		SCIP_Real *RESTRICT	lincoefx,
		SCIP_Real *RESTRICT	lincoefy,
		SCIP_Real *RESTRICT	linconstant,
		SCIP_Bool *RESTRICT	success
	)

computes coefficients of linearization of a bilinear term in a reference point when given two linear inequality involving only the variables of the bilinear term

Note

the formulas are extracted from "Convex envelopes of bivariate functions through the solution of KKT systems" by Marco Locatelli

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
xcoef1	x coefficient of linear inequality; must be in {-1,0,1}
ycoef1	y coefficient of linear inequality
constant1	constant of linear inequality
xcoef2	x coefficient of linear inequality; must be in {-1,0,1}
ycoef2	y coefficient of linear inequality
constant2	constant of linear inequality
lincoefx	buffer to store coefficient of first variable in linearization
lincoefy	buffer to store coefficient of second variable in linearization
linconstant	buffer to store constant of linearization
success	buffer to store whether linearization was successful

Definition at line 825 of file scip_nonlinear.c.

References computeBilinEnvelope2(), FALSE, NULL, SCIP_INVALID, SCIP_Real, SCIPisEQ(), SCIPisFeasEQ(), SCIPisFeasGE(), SCIPisFeasGT(), SCIPisFeasLE(), SCIPisGE(), SCIPisInfinity(), SCIPisLE(), SCIPisNegative(), and SCIPisRelEQ().

Referenced by updateBilinearRelaxation().

SCIPcreateNlpiProb()

SCIP_EXPORT SCIP_RETCODE SCIPcreateNlpiProb	(	SCIP *	scip,
		SCIP_NLPI *	nlpi,
		SCIP_NLROW **	nlrows,
		int	nnlrows,
		SCIP_NLPIPROBLEM *	nlpiprob,
		SCIP_HASHMAP *	var2idx,
		SCIP_Real *	nlscore,
		SCIP_Real	cutoffbound,
		SCIP_Bool	setobj,
		SCIP_Bool	onlyconvex
	)

creates an NLP relaxation and stores it in a given NLPI problem; the function computes for each variable which the number of non-linearly occurrences and stores it in the nlscore array

Note

the first row corresponds always to the cutoff row (even if cutoffbound is SCIPinfinity(scip))

Parameters

scip	SCIP data structure
nlpi	interface to NLP solver
nlrows	nonlinear rows
nnlrows	total number of nonlinear rows
nlpiprob	empty nlpi problem
var2idx	empty hash map to store mapping between variables and indices in nlpi problem
nlscore	array to store the score of each nonlinear variable (NULL if not needed)
cutoffbound	cutoff bound
setobj	should the objective function be set?
onlyconvex	filter only for convex constraints

Definition at line 958 of file scip_nonlinear.c.

References BMSclearMemoryArray, SCIP_QuadElement::coef, FALSE, SCIP_QuadElement::idx1, SCIP_QuadElement::idx2, NULL, SCIP_Bool, SCIP_CALL, SCIP_EXPRCURV_CONCAVE, SCIP_EXPRCURV_CONVEX, SCIP_OKAY, SCIP_Real, SCIPallocBufferArray, SCIPdebugMsg, SCIPexprtreeGetNVars(), SCIPexprtreeGetVars(), SCIPfreeBufferArray, SCIPgetNVars(), SCIPgetVars(), SCIPhashmapExists(), SCIPhashmapGetImageInt(), SCIPhashmapInsertInt(), SCIPinfinity(), SCIPisInfinity(), SCIPisZero(), SCIPnlpiAddConstraints(), SCIPnlpiAddVars(), SCIPnlpiSetObjective(), SCIPnlrowGetConstant(), SCIPnlrowGetCurvature(), SCIPnlrowGetExprtree(), SCIPnlrowGetLhs(), SCIPnlrowGetLinearCoefs(), SCIPnlrowGetLinearVars(), SCIPnlrowGetName(), SCIPnlrowGetNLinearVars(), SCIPnlrowGetNQuadElems(), SCIPnlrowGetQuadElems(), SCIPnlrowGetQuadVars(), SCIPnlrowGetRhs(), SCIPswapInts(), SCIPvarGetLbLocal(), SCIPvarGetName(), SCIPvarGetObj(), SCIPvarGetUbLocal(), and TRUE.

Referenced by applyNlobbt(), computeInteriorPoint(), createNLP(), SCIP_DECL_RELAXEXEC(), and SCIP_DECL_SEPAEXECLP().

SCIPupdateNlpiProb()

SCIP_EXPORT SCIP_RETCODE SCIPupdateNlpiProb	(	SCIP *	scip,
		SCIP_NLPI *	nlpi,
		SCIP_NLPIPROBLEM *	nlpiprob,
		SCIP_HASHMAP *	var2nlpiidx,
		SCIP_VAR **	nlpivars,
		int	nlpinvars,
		SCIP_Real	cutoffbound
	)

updates bounds of each variable and the cutoff row in the nlpiproblem

Parameters

scip	SCIP data structure
nlpi	interface to NLP solver
nlpiprob	nlpi problem representing the convex NLP relaxation
var2nlpiidx	mapping between variables and nlpi indices
nlpivars	array containing all variables of the nlpi
nlpinvars	total number of nlpi variables
cutoffbound	new cutoff bound

Definition at line 1281 of file scip_nonlinear.c.

References NULL, SCIP_CALL, SCIP_OKAY, SCIP_Real, SCIPallocBufferArray, SCIPdebugMsg, SCIPfreeBufferArray, SCIPhashmapExists(), SCIPhashmapGetImageInt(), SCIPinfinity(), SCIPnlpiChgConsSides(), SCIPnlpiChgVarBounds(), SCIPvarGetLbLocal(), and SCIPvarGetUbLocal().

Referenced by applyNlobbt(), and SCIP_DECL_SEPAEXECLP().

SCIPaddNlpiProbRows()

SCIP_EXPORT SCIP_RETCODE SCIPaddNlpiProbRows	(	SCIP *	scip,
		SCIP_NLPI *	nlpi,
		SCIP_NLPIPROBLEM *	nlpiprob,
		SCIP_HASHMAP *	var2idx,
		SCIP_ROW **	rows,
		int	nrows
	)

adds linear rows to the NLP relaxation

Parameters

scip	SCIP data structure
nlpi	interface to NLP solver
nlpiprob	nlpi problem
var2idx	empty hash map to store mapping between variables and indices in nlpi problem
rows	rows to add
nrows	total number of rows to add

Definition at line 1333 of file scip_nonlinear.c.

References NULL, SCIP_CALL, SCIP_OKAY, SCIP_Real, SCIPallocBufferArray, SCIPcolGetVar(), SCIPdebugMsg, SCIPfreeBufferArray, SCIPgetNVars(), SCIPhashmapExists(), SCIPhashmapGetImageInt(), SCIPnlpiAddConstraints(), SCIProwGetCols(), SCIProwGetConstant(), SCIProwGetLhs(), SCIProwGetName(), SCIProwGetNNonz(), SCIProwGetRhs(), and SCIProwGetVals().

Referenced by applyNlobbt(), computeInteriorPoint(), SCIP_DECL_RELAXEXEC(), and SCIP_DECL_SEPAEXECLP().