Detailed Description

methods for nonlinear data

Functions
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)

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)

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

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

Nonlinear Methods
static void	computeBilinEnvelope2 (SCIP scip, SCIP_Real x, SCIP_Real y, SCIP_Real mi, SCIP_Real qi, SCIP_Real mj, SCIP_Real qj, SCIP_Real RESTRICT xi, SCIP_Real RESTRICT yi, SCIP_Real RESTRICT xj, SCIP_Real RESTRICT yj, SCIP_Real RESTRICT xcoef, SCIP_Real RESTRICT ycoef, SCIP_Real RESTRICT constant)

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 33285 of file scip.c.

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

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

◆ SCIPaddSquareSecant()

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 33353 of file scip.c.

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

Referenced by addBilinearTermToCut(), and generateCutNonConvex().

◆ SCIPaddBilinLinearization()

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 33403 of file scip.c.

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

Referenced by generateCutConvex().

◆ SCIPaddBilinMcCormick()

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 33450 of file scip.c.

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

Referenced by addBilinearTermToCut(), and generateCutNonConvex().

◆ SCIPcomputeBilinEnvelope1()

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 33659 of file scip.c.

References FALSE, SCIP_INVALID, SCIP_Real, SCIPisFeasEQ(), SCIPisFeasGE(), SCIPisFeasGT(), SCIPisFeasLE(), SCIPisGE(), SCIPisInfinity(), SCIPisLE(), SCIPisNegative(), and SCIPisZero().

Referenced by updateBilinearRelaxation().

◆ SCIPcomputeBilinEnvelope2()

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 33893 of file scip.c.

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

Referenced by updateBilinearRelaxation().

◆ SCIPcreateNlpiProb()

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 34026 of file scip.c.

References BMSclearMemoryArray, SCIP_QuadElement::coef, FALSE, SCIP_QuadElement::idx1, SCIP_QuadElement::idx2, SCIP_Bool, SCIP_CALL, SCIP_EXPRCURV_CONCAVE, SCIP_EXPRCURV_CONVEX, SCIP_OKAY, SCIP_Real, SCIPallocBufferArray, SCIPdebugMsg, SCIPexprtreeGetNVars(), SCIPexprtreeGetVars(), SCIPfreeBufferArray, SCIPgetNVars(), SCIPgetVars(), SCIPhashmapExists(), SCIPhashmapGetImage(), SCIPhashmapInsert(), 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_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 34349 of file scip.c.

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

Referenced by applyNlobbt(), and SCIP_DECL_SEPAEXECLP().

◆ SCIPaddNlpiProbRows()

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 34401 of file scip.c.

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

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

◆ computeBilinEnvelope2()

static void computeBilinEnvelope2	(	SCIP *	scip,
		SCIP_Real	x,
		SCIP_Real	y,
		SCIP_Real	mi,
		SCIP_Real	qi,
		SCIP_Real	mj,
		SCIP_Real	qj,
		SCIP_Real *RESTRICT	xi,
		SCIP_Real *RESTRICT	yi,
		SCIP_Real *RESTRICT	xj,
		SCIP_Real *RESTRICT	yj,
		SCIP_Real *RESTRICT	xcoef,
		SCIP_Real *RESTRICT	ycoef,
		SCIP_Real *RESTRICT	constant
	)

static

helper function to compute the convex envelope of a bilinear term when two linear inequalities are given; we use the same notation and formulas as in Locatelli 2016

Parameters

scip	SCIP data structure
x	reference point for x
y	reference point for y
mi	coefficient of x in the first linear inequality
qi	constant in the first linear inequality
mj	coefficient of x in the second linear inequality
qj	constant in the second linear inequality
xi	buffer to store x coordinate of the first point
yi	buffer to store y coordinate of the first point
xj	buffer to store x coordinate of the second point
yj	buffer to store y coordinate of the second point
xcoef	buffer to store the x coefficient of the envelope
ycoef	buffer to store the y coefficient of the envelope
constant	buffer to store the constant of the envelope

Definition at line 33824 of file scip.c.

References REALABS, and SCIPisEQ().

Referenced by SCIPcomputeBilinEnvelope2().

SCIP

Detailed Description

Functions

Nonlinear Methods

Function Documentation

◆ SCIPaddSquareLinearization()

◆ SCIPaddSquareSecant()

◆ SCIPaddBilinLinearization()

◆ SCIPaddBilinMcCormick()

◆ SCIPcomputeBilinEnvelope1()

◆ SCIPcomputeBilinEnvelope2()

◆ SCIPcreateNlpiProb()

◆ SCIPupdateNlpiProb()

◆ SCIPaddNlpiProbRows()

◆ computeBilinEnvelope2()