Constraint handler for SDP-constraints. More...

Functions
SCIP_EXPORT SCIP_RETCODE	SCIPincludeConshdlrSdp (SCIP *scip)

SCIP_EXPORT SCIP_RETCODE	SCIPincludeConshdlrSdpRank1 (SCIP *scip)

SCIP_EXPORT SCIP_RETCODE	SCIPcreateConsSdp (SCIP scip, SCIP_CONS cons, const char name, int nvars, int nnonz, int blocksize, int nvarnonz, int col, int row, SCIP_Real val, SCIP_VAR vars, int constnnonz, int constcol, int constrow, SCIP_Real constval)

SCIP_EXPORT SCIP_RETCODE	SCIPcreateConsSdpRank1 (SCIP scip, SCIP_CONS cons, const char name, int nvars, int nnonz, int blocksize, int nvarnonz, int col, int row, SCIP_Real val, SCIP_VAR vars, int constnnonz, int constcol, int constrow, SCIP_Real constval)

SCIP_EXPORT int	SCIPconsSdpCompLowerTriangPos (int i, int j)

SCIP_EXPORT SCIP_RETCODE	SCIPconsSdpGetData (SCIP scip, SCIP_CONS cons, int nvars, int nnonz, int blocksize, int arraylength, int nvarnonz, int col, int row, SCIP_Real val, SCIP_VAR vars, int constnnonz, int constcol, int constrow, SCIP_Real constval, SCIP_Bool rankone, int *maxevsubmat, SCIP_Bool addedquadcons)

SCIP_EXPORT SCIP_RETCODE	SCIPconsSdpGetNNonz (SCIP scip, SCIP_CONS cons, int nnonz, int constnnonz)

SCIP_EXPORT int	SCIPconsSdpGetBlocksize (SCIP scip, SCIP_CONS cons)

SCIP_EXPORT SCIP_RETCODE	SCIPconsSdpGetFullAj (SCIP scip, SCIP_CONS cons, int j, SCIP_Real *Aj)

SCIP_EXPORT SCIP_RETCODE	SCIPconsSdpGetFullConstMatrix (SCIP scip, SCIP_CONS cons, SCIP_Real *mat)

SCIP_EXPORT SCIP_RETCODE	SCIPconsSdpGetLowerTriangConstMatrix (SCIP scip, SCIP_CONS cons, SCIP_Real *mat)

SCIP_EXPORT SCIP_RETCODE	SCIPconsSdpCheckSdpCons (SCIP scip, SCIP_CONS cons, SCIP_SOL sol, SCIP_Bool printreason, SCIP_RESULT result)

SCIP_EXPORT SCIP_RETCODE	SCIPconsSdpGuessInitialPoint (SCIP scip, SCIP_CONS cons, SCIP_Real *lambdastar)

SCIP_EXPORT SCIP_Real	SCIPconsSdpGetMaxConstEntry (SCIP scip, SCIP_CONS cons)

SCIP_EXPORT SCIP_Real	SCIPconsSdpGetMaxSdpCoef (SCIP scip, SCIP_CONS cons)

SCIP_EXPORT int	SCIPconsSdpComputeUbSparseSdpMatrixLength (SCIP_CONS *cons)

SCIP_EXPORT SCIP_RETCODE	SCIPconsSdpComputeSparseSdpMatrix (SCIP scip, SCIP_CONS cons, SCIP_SOL sol, int length, int row, int col, SCIP_Real *val)

SCIP_EXPORT SCIP_Bool	SCIPconsSdpShouldBeRankOne (SCIP_CONS *cons)

SCIP_EXPORT SCIP_RETCODE	SCIPconsSdpGetMaxEVSubmat (SCIP_CONS cons, int *maxevsubmat)

SCIP_EXPORT SCIP_Bool	SCIPconsSdpAddedQuadCons (SCIP_CONS *cons)

Detailed Description

Constraint handler for SDP-constraints.

Author: Sonja Mars; Lars Schewe; Tristan Gally

Constraint handler for semidefinite constraints of the form $\sum_{j=1}^n A_j y_j - A_0 \succeq 0$ , where the matrices $A_j$ and $A_0$ need to be symmetric. Only the nonzero entries of the matrices are stored.

Definition in file cons_sdp.h.

Function Documentation

SCIP_EXPORT SCIP_RETCODE SCIPincludeConshdlrSdp ( SCIP * scip )

creates the handler for SDP constraints and includes it in SCIP

Parameters

scip	SCIP data structure

Definition at line 4420 of file cons_sdp.c.

References CONSHDLR_CHECKPRIORITY, CONSHDLR_DELAYSEPA, CONSHDLR_DESC, CONSHDLR_EAGERFREQ, CONSHDLR_ENFOPRIORITY, CONSHDLR_MAXPREROUNDS, CONSHDLR_NAME, CONSHDLR_NEEDSCONS, CONSHDLR_PRESOLTIMING, CONSHDLR_SEPAFREQ, CONSHDLR_SEPAPRIORITY, DEFAULT_DIAGGEZEROCUTS, DEFAULT_DIAGZEROIMPLCUTS, DEFAULT_MAXNVARSQUADUPGD, DEFAULT_QUADCONSRANK1, DEFAULT_RANK1APPROXHEUR, DEFAULT_TWOMINORLINCONSS, DEFAULT_TWOMINORPRODCONSS, DEFAULT_UPGRADEKEEPQUAD, DEFAULT_UPGRADQUADCONSS, and SCIPincludeConshdlrSdpRank1().

Referenced by SCIP_DECL_CONSGETNVARS(), SCIP_DECL_CONSHDLRCOPY(), and SCIPSDPincludeDefaultPlugins().

SCIP_EXPORT SCIP_RETCODE SCIPincludeConshdlrSdpRank1 ( SCIP * scip )

creates the handler for rank 1 SDP constraints and includes it in SCIP

Parameters

scip	SCIP data structure

Definition at line 4513 of file cons_sdp.c.

References CONSHDLR_CHECKPRIORITY, CONSHDLR_DELAYSEPA, CONSHDLR_EAGERFREQ, CONSHDLR_ENFOPRIORITY, CONSHDLR_MAXPREROUNDS, CONSHDLR_NAME, CONSHDLR_NEEDSCONS, CONSHDLR_PRESOLTIMING, CONSHDLR_SEPAFREQ, CONSHDLR_SEPAPRIORITY, CONSHDLRRANK1_DESC, CONSHDLRRANK1_NAME, and SCIPconsSdpCompLowerTriangPos().

Referenced by SCIP_DECL_CONSHDLRCOPY(), SCIPincludeConshdlrSdp(), and SCIPSDPincludeDefaultPlugins().

SCIP_EXPORT SCIP_RETCODE SCIPcreateConsSdp	(	SCIP *	scip,
		SCIP_CONS **	cons,
		const char *	name,
		int	nvars,
		int	nnonz,
		int	blocksize,
		int *	nvarnonz,
		int **	col,
		int **	row,
		SCIP_Real **	val,
		SCIP_VAR **	vars,
		int	constnnonz,
		int *	constcol,
		int *	constrow,
		SCIP_Real *	constval
	)

creates an SDP-constraint

Parameters

scip	SCIP data structure
cons	pointer to hold the created constraint
name	name of constraint
nvars	number of variables in this SDP constraint
nnonz	number of nonzeros in this SDP constraint
blocksize	size of this SDP-block
nvarnonz	number of nonzeros for each variable, also length of the arrays col/row/val point to
col	pointer to column indices of the nonzeros for each variable
row	pointer to row indices of the nonzeros for each variable
val	pointer to values of the nonzeros for each variable
vars	SCIP_VARiables present in this SDP constraint that correspond to the indices in col/row/val
constnnonz	number of nonzeros in the constant part of this SDP constraint
constcol	column indices of the constant nonzeros
constrow	row indices of the constant nonzeros
constval	values of the constant nonzeros

Definition at line 5150 of file cons_sdp.c.

References name, SCIPcreateConsSdpRank1(), and setMaxRhsEntry().

Referenced by SCIP_DECL_CONSCOPY(), SCIP_DECL_QUADCONSUPGD(), scip::SCIP_DECL_READERREAD(), and SCIPconsSdpAddedQuadCons().

SCIP_EXPORT SCIP_RETCODE SCIPcreateConsSdpRank1	(	SCIP *	scip,
		SCIP_CONS **	cons,
		const char *	name,
		int	nvars,
		int	nnonz,
		int	blocksize,
		int *	nvarnonz,
		int **	col,
		int **	row,
		SCIP_Real **	val,
		SCIP_VAR **	vars,
		int	constnnonz,
		int *	constcol,
		int *	constrow,
		SCIP_Real *	constval
	)

creates a rank 1 SDP-constraint

Parameters

scip	SCIP data structure
cons	pointer to hold the created constraint
name	name of constraint
nvars	number of variables in this SDP constraint
nnonz	number of nonzeros in this SDP constraint
blocksize	size of this SDP-block
nvarnonz	number of nonzeros for each variable, also length of the arrays col/row/val point to
col	pointer to column indices of the nonzeros for each variable
row	pointer to row indices of the nonzeros for each variable
val	pointer to values of the nonzeros for each variable
vars	SCIP_VARiables present in this SDP constraint that correspond to the indices in col/row/val
constnnonz	number of nonzeros in the constant part of this SDP constraint
constcol	column indices of the constant nonzeros
constrow	row indices of the constant nonzeros
constval	values of the constant nonzeros

Definition at line 5269 of file cons_sdp.c.

References CONSHDLRRANK1_NAME, name, and setMaxRhsEntry().

Referenced by SCIP_DECL_CONSCOPY(), SCIP_DECL_QUADCONSUPGD(), and SCIPcreateConsSdp().

SCIP_EXPORT int SCIPconsSdpCompLowerTriangPos	(	int	i,
		int	j
	)

for given row and column (i,j) computes the position in the lower triangular part, if these positions are numbered from 0 to n(n+1)/2 - 1, this needs to be called for i >= j

Parameters

i	row index
j	column index

Definition at line 4585 of file cons_sdp.c.

References SCIPconsSdpGetData().

Referenced by calcRelax(), computeSdpMatrix(), diagGEzero(), expandSymMatrix(), isMatrixRankOne(), SCIP_DECL_CONSINITSOL(), SCIPconsSdpGetLowerTriangConstMatrix(), and SCIPincludeConshdlrSdpRank1().

SCIP_EXPORT SCIP_RETCODE SCIPconsSdpGetData	(	SCIP *	scip,
		SCIP_CONS *	cons,
		int *	nvars,
		int *	nnonz,
		int *	blocksize,
		int *	arraylength,
		int *	nvarnonz,
		int **	col,
		int **	row,
		SCIP_Real **	val,
		SCIP_VAR **	vars,
		int *	constnnonz,
		int *	constcol,
		int *	constrow,
		SCIP_Real *	constval,
		SCIP_Bool *	rankone,
		int **	maxevsubmat,
		SCIP_Bool *	addedquadcons
	)

get the data belonging to a single SDP-constraint

In arraylength the length of the nvarnonz, col, row and val arrays has to be given, if it is not sufficient to store all block-pointers that need to be inserted, a debug message will be thrown and this variable will be set to the needed length. constnnonz should give the length of the const arrays, if it is too short it will also give the needed number and a debug message is thrown.

get the data belonging to a single SDP-constraint

In arraylength the length of the nvarnonz, col, row and val arrays has to be given, if it is not sufficient to store all block-pointers that need to be inserted, a debug message will be thrown and this variable will be set to the needed length. constnnonz should give the length of the const arrays, if it is too short it will also give the needed number and a debug message is thrown. rankone and maxevsubmat can be NULL-pointers, if the corresponding information is not needed.

Parameters

scip	SCIP data structure
cons	SDP constraint to get data of
nvars	pointer to store the number of variables in this SDP constraint
nnonz	pointer to store the number of nonzeros in this SDP constraint
blocksize	pointer to store the size of this SDP-block
arraylength	length of the given nvarnonz, col, row and val arrays, if this is too short this will return the needed length
nvarnonz	pointer to store the number of nonzeros for each variable, also length of the arrays col/row/val are pointing to
col	pointer to store the column indices of the nonzeros for each variable
row	pointer to store the row indices of the nonzeros for each variable
val	pointer to store the values of the nonzeros for each variable
vars	pointer to store the SCIP variables present in this constraint that correspond to the indices in col/row/val
constnnonz	pointer to store the number of nonzeros in the constant part of this SDP constraint, also length of the const arrays
constcol	pointer to store the column indices of the constant nonzeros
constrow	pointer to store the row indices of the constant nonzeros
constval	pointer to store the values of the constant nonzeros
rankone	pointer to store if matrix should be rank one (or NULL, if information not necessary)
maxevsubmat	pointer to store two row indices of 2x2 subdeterminant with maximal eigenvalue [-1,-1 if not yet computed] (or NULL, if information not necessary)
addedquadcons	pointer to store if the quadratic 2x2-minor constraints already added (in the rank1-case) (or NULL, if information not necessary)

Definition at line 4603 of file cons_sdp.c.

References SCIPconsSdpGetNNonz().

Referenced by calcRelax(), putSdpDataInInterface(), and SCIPconsSdpCompLowerTriangPos().

SCIP_EXPORT SCIP_RETCODE SCIPconsSdpGetNNonz	(	SCIP *	scip,
		SCIP_CONS *	cons,
		int *	nnonz,
		int *	constnnonz
	)

gets the number of nonzeros and constant nonzeros for this SDP constraint

Either nnonz or constnnonz may be NULL if only the other one is needed.

Parameters

scip	SCIP data structure
cons	SDP constraint to get number of nonzeros for
nnonz	pointer to store the number of nonzeros in this SDP constraint
constnnonz	pointer to store the number of nonzeros in the constant part of this SDP constraint

Definition at line 4710 of file cons_sdp.c.

References SCIPconsSdpGetBlocksize().

Referenced by calcRelax(), putSdpDataInInterface(), and SCIPconsSdpGetData().

SCIP_EXPORT int SCIPconsSdpGetBlocksize	(	SCIP *	scip,
		SCIP_CONS *	cons
	)

gets the blocksize of the SDP constraint

Parameters

scip	SCIP data structure
cons	SDP constraint to get blocksize for

Definition at line 4735 of file cons_sdp.c.

References SCIPconsSdpGetFullAj().

Referenced by calcRelax(), SCIPconsSdpGetNNonz(), and SCIPrelaxSdpComputeAnalyticCenters().

SCIP_EXPORT SCIP_RETCODE SCIPconsSdpGetFullAj	(	SCIP *	scip,
		SCIP_CONS *	cons,
		int	j,
		SCIP_Real *	Aj
	)

gets the full constraint Matrix $ A_j $ for a given variable j

Parameters

scip	SCIP data structure
cons	SDP constraint to get matrix for
j	the variable j to get the corresponding matrix for
Aj	pointer to store the full matrix

Definition at line 4752 of file cons_sdp.c.

References SCIPconsSdpGetFullConstMatrix().

Referenced by addTwoMinorLinConstraints(), addTwoMinorProdConstraints(), checkVarsLocks(), SCIP_DECL_CONSCHECK(), SCIP_DECL_CONSINITSOL(), SCIP_DECL_CONSLOCK(), SCIPconsSdpGetBlocksize(), and updateVarLocks().

SCIP_EXPORT SCIP_RETCODE SCIPconsSdpGetFullConstMatrix	(	SCIP *	scip,
		SCIP_CONS *	cons,
		SCIP_Real *	mat
	)

gives an n*n-long array with the full constant matrix

Parameters

scip	SCIP data structure
cons	SDP constraint to get matrix for
mat	pointer to store the full constant matrix

Definition at line 4787 of file cons_sdp.c.

References SCIPconsSdpGetLowerTriangConstMatrix().

Referenced by addTwoMinorLinConstraints(), addTwoMinorProdConstraints(), cutUsingEigenvector(), SCIP_DECL_CONSCHECK(), and SCIPconsSdpGetFullAj().

SCIP_EXPORT SCIP_RETCODE SCIPconsSdpGetLowerTriangConstMatrix	(	SCIP *	scip,
		SCIP_CONS *	cons,
		SCIP_Real *	mat
	)

gives a 0.5*n*(n+1)-long array with the lower triangular part of the constant matrix indexed by SCIPconsSdpCompLowerTriangPos

Parameters

scip	SCIP data structure
cons	SDP constraint to get data of
mat	pointer to store the lower triangular part of the constant matrix

Definition at line 4821 of file cons_sdp.c.

References SCIPconsSdpCompLowerTriangPos(), and SCIPconsSdpGuessInitialPoint().

Referenced by diagGEzero(), SCIP_DECL_CONSINITSOL(), and SCIPconsSdpGetFullConstMatrix().

SCIP_EXPORT SCIP_RETCODE SCIPconsSdpCheckSdpCons	(	SCIP *	scip,
		SCIP_CONS *	cons,
		SCIP_SOL *	sol,
		SCIP_Bool	printreason,
		SCIP_RESULT *	result
	)

checks feasibility for a single SDP constraint

Parameters

scip	SCIP data structure
cons	the constraint the solution should be checked for
sol	the solution to check feasibility for
printreason	should the reason for the violation be printed?
result	pointer to store the result of the feasibility checking call

Definition at line 540 of file cons_sdp.c.

References computeSdpMatrix(), CONSHDLR_NAME, CONSHDLRRANK1_NAME, expandSymMatrix(), SCIPlapackComputeIthEigenvalue(), and separateSol().

Referenced by cutUsingEigenvector(), enforceConstraint(), isMatrixRankOne(), SCIP_DECL_CONSCHECK(), and SCIP_DECL_CONSENFOPS().

SCIP_EXPORT SCIP_RETCODE SCIPconsSdpGuessInitialPoint	(	SCIP *	scip,
		SCIP_CONS *	cons,
		SCIP_Real *	lambdastar
	)

Compute a heuristic guess for a good starting solution $\lambda ^* \cdot I$ .

The solution is computed as

$\lambda^* = \max \Bigg\{S \cdot \max_{i \in [m]} \{|u_i|, |l_i|\} \cdot \max_{i \in [m]} \|A_i\|_\infty + \|C\|_\infty, \frac{\max_{i \in [m]} b_i}{S \cdot \min_{i \in [m]} \min_{j, \ell \in [n]} (A_i)_{j\ell} } \Bigg\},$

where $S = \frac{ | \text{nonzero-entries of all } A_i | }{0.5 \cdot \text{ blocksize } (\text{ blocksize } + 1)}$ measures the sparsity of the matrices.

Parameters

scip	SCIP data structure
cons	the constraint for which the initial point should be constructed
lambdastar	pointer to store the guess for the initial point

Definition at line 4860 of file cons_sdp.c.

References CONSHDLR_NAME, CONSHDLRRANK1_NAME, and SCIPconsSdpGetMaxConstEntry().

Referenced by SCIP_DECL_RELAXINITSOL(), and SCIPconsSdpGetLowerTriangConstMatrix().

SCIP_EXPORT SCIP_Real SCIPconsSdpGetMaxConstEntry	(	SCIP *	scip,
		SCIP_CONS *	cons
	)

Gets maximum absolute entry of constant matrix $ A_0 $

Parameters

scip	SCIP data structure
cons	the constraint to get the maximum constant matrix entry for

Definition at line 4956 of file cons_sdp.c.

References SCIPconsSdpGetMaxSdpCoef().

Referenced by SCIP_DECL_RELAXINITSOL(), and SCIPconsSdpGuessInitialPoint().

SCIP_EXPORT SCIP_Real SCIPconsSdpGetMaxSdpCoef	(	SCIP *	scip,
		SCIP_CONS *	cons
	)

Gets maximum absolute entry of all matrices $ A_i $

Parameters

scip	SCIP data structure
cons	the constraint to get the maximum constant matrix entry for

Definition at line 4972 of file cons_sdp.c.

References SCIPconsSdpComputeUbSparseSdpMatrixLength().

Referenced by SCIP_DECL_RELAXINITSOL(), and SCIPconsSdpGetMaxConstEntry().

SCIP_EXPORT int SCIPconsSdpComputeUbSparseSdpMatrixLength ( SCIP_CONS * cons )

Computes an upper bound on the number of nonzeros of the (dual) SDP matrix $Z = \sum_{j=1}^n A_j y_j - A_0$ , this should be used to allocate enough memory before calling SCIPconsSdpComputeSparseSdpMatrix.

Upper bound is computed as $\min \{ \sum_{v \leq m} \text{nvarnonz}(v) + \text{constnnonz}, n \cdot (n+1) / 2 \}$ .

Parameters

cons	the constraint for which the Matrix should be assembled

Definition at line 5006 of file cons_sdp.c.

References SCIPconsSdpComputeSparseSdpMatrix().

Referenced by calcRelax(), SCIPconsSdpGetMaxSdpCoef(), and SCIPrelaxSdpComputeAnalyticCenters().

SCIP_EXPORT SCIP_RETCODE SCIPconsSdpComputeSparseSdpMatrix	(	SCIP *	scip,
		SCIP_CONS *	cons,
		SCIP_SOL *	sol,
		int *	length,
		int *	row,
		int *	col,
		SCIP_Real *	val
	)

Computes (dual) SDP matrix $Z = \sum_{j=1}^n A_j y_j - A_0$ and returns it in sparse format

Note: row, col and val should have memory allocated equal to SCIPconsSdpComputeUbSparseSdpMatrixLength(), if the memory is not sufficient, length will be set to -1 and an error will be thrown

Parameters

scip	SCIP data structure
cons	the constraint for which the Matrix should be assembled
sol	the solution to assemble the matrix for
length	input: allocated memory for row/col/val arrays output: number of nonzeros of the matrix / length of row/col/val arrays
row	pointer to store row indices of SDP-matrix
col	pointer to store column indices of SDP-matrix
val	pointer to store values of SDP-matrix

Definition at line 5034 of file cons_sdp.c.

References SCIPconsSdpShouldBeRankOne(), and SCIPsdpVarfixerMergeArrays().

Referenced by calcRelax(), SCIPconsSdpComputeUbSparseSdpMatrixLength(), and SCIPrelaxSdpComputeAnalyticCenters().

SCIP_EXPORT SCIP_Bool SCIPconsSdpShouldBeRankOne ( SCIP_CONS * cons )

returns wheter matrix should be rank one

returns whether the matrix should be rank one

Parameters

cons	the constraint for which the existence of a rank one constraint should be checked

Definition at line 5099 of file cons_sdp.c.

References SCIPconsSdpGetMaxEVSubmat().

Referenced by SCIPconsSdpComputeSparseSdpMatrix().

SCIP_EXPORT SCIP_RETCODE SCIPconsSdpGetMaxEVSubmat	(	SCIP_CONS *	cons,
		int **	maxevsubmat
	)

returns two row indices of 2x2 subdeterminant with maximal eigenvalue [or -1,-1 if not available]

Parameters

cons	the constraint for which the existence of a rank one constraint should be checked
maxevsubmat	pointer to store the two row indices of 2x2 subdeterminant with maximal eigenvalue [or -1,-1 if not available]

Definition at line 5114 of file cons_sdp.c.

References SCIPconsSdpAddedQuadCons().

Referenced by SCIPconsSdpShouldBeRankOne().

SCIP_EXPORT SCIP_Bool SCIPconsSdpAddedQuadCons ( SCIP_CONS * cons )

returns whether the quadratic 2x2-minor constraints are already added (in the rank1-case)

Parameters

cons	the constraint for which it should be checked whether the quadratic 2x2-minor constraints are already added (in the rank1-case)

Definition at line 5135 of file cons_sdp.c.

References SCIPcreateConsSdp().

Referenced by SCIPconsSdpGetMaxEVSubmat().

Functions

Detailed Description

Function Documentation