interface for SDPA More...

Macros
#define	EPSILONCHANGE 1

#define	FEASTOLCHANGE 1

#define	PENALTYBOUNDTOL 1E-3

#define	MIN_LAMBDASTAR 1e0

#define	MAX_LAMBDASTAR 1e8

#define	LAMBDASTAR_FACTOR 1e0

#define	LAMBDASTAR_TWOPOINTS TRUE

#define	LAMBDASTAR_THRESHOLD 1e1

#define	LAMBDASTAR_LOW 1.5

#define	LAMBDASTAR_HIGH 1e5

#define	MIN_PENALTYPARAM 1e5

#define	MAX_PENALTYPARAM 1e12

#define	PENALTYPARAM_FACTOR 1e1

#define	MAX_MAXPENALTYPARAM 1e15

#define	MAXPENALTYPARAM_FACTOR 1e6

#define	BMS_CALL(x)

#define	CHECK_IF_SOLVED(sdpisolver)

#define	CHECK_IF_SOLVED_BOOL(sdpisolver)

Functions
static SCIP_Bool	isFixed (SCIP_SDPISOLVER *sdpisolver, SCIP_Real lb, SCIP_Real ub)

Miscellaneous Methods
const char *	SCIPsdpiSolverGetSolverName (void)

const char *	SCIPsdpiSolverGetSolverDesc (void)

void *	SCIPsdpiSolverGetSolverPointer (SCIP_SDPISOLVER *sdpisolver)

SDPI Creation and Destruction Methods
SCIP_RETCODE	SCIPsdpiSolverCreate (SCIP_SDPISOLVER *sdpisolver, SCIP_MESSAGEHDLR messagehdlr, BMS_BLKMEM *blkmem)

SCIP_RETCODE	SCIPsdpiSolverFree (SCIP_SDPISOLVER **sdpisolver)

SCIP_RETCODE	SCIPsdpiSolverIncreaseCounter (SCIP_SDPISOLVER *sdpisolver)

SCIP_RETCODE	SCIPsdpiSolverResetCounter (SCIP_SDPISOLVER *sdpisolver)

Solving Methods
SCIP_RETCODE	SCIPsdpiSolverLoadAndSolve (SCIP_SDPISOLVER sdpisolver, int nvars, SCIP_Real obj, SCIP_Real lb, SCIP_Real ub, int nsdpblocks, int sdpblocksizes, int sdpnblockvars, int sdpconstnnonz, int sdpconstnblocknonz, int sdpconstrow, int sdpconstcol, SCIP_Real sdpconstval, int sdpnnonz, int sdpnblockvarnonz, int sdpvar, int sdprow, int sdpcol, SCIP_Real sdpval, int indchanges, int nremovedinds, int blockindchanges, int nremovedblocks, int nlpcons, int noldlpcons, SCIP_Real lplhs, SCIP_Real lprhs, int lprownactivevars, int lpnnonz, int lprow, int lpcol, SCIP_Real lpval, SCIP_Real *start, SCIP_SDPSOLVERSETTING startsettings, SCIP_Real timelimit)

SCIP_RETCODE	SCIPsdpiSolverLoadAndSolveWithPenalty (SCIP_SDPISOLVER sdpisolver, SCIP_Real penaltyparam, SCIP_Bool withobj, SCIP_Bool rbound, int nvars, SCIP_Real obj, SCIP_Real lb, SCIP_Real ub, int nsdpblocks, int sdpblocksizes, int sdpnblockvars, int sdpconstnnonz, int sdpconstnblocknonz, int sdpconstrow, int sdpconstcol, SCIP_Real sdpconstval, int sdpnnonz, int sdpnblockvarnonz, int sdpvar, int sdprow, int sdpcol, SCIP_Real sdpval, int indchanges, int nremovedinds, int blockindchanges, int nremovedblocks, int nlpcons, int noldlpcons, SCIP_Real lplhs, SCIP_Real lprhs, int rownactivevars, int lpnnonz, int lprow, int lpcol, SCIP_Real lpval, SCIP_Real start, SCIP_SDPSOLVERSETTING startsettings, SCIP_Real timelimit, SCIP_Bool feasorig, SCIP_Bool *penaltybound)

Solution Information Methods
SCIP_Bool	SCIPsdpiSolverWasSolved (SCIP_SDPISOLVER *sdpisolver)

SCIP_Bool	SCIPsdpiSolverFeasibilityKnown (SCIP_SDPISOLVER *sdpisolver)

SCIP_RETCODE	SCIPsdpiSolverGetSolFeasibility (SCIP_SDPISOLVER sdpisolver, SCIP_Bool primalfeasible, SCIP_Bool *dualfeasible)

SCIP_Bool	SCIPsdpiSolverIsPrimalUnbounded (SCIP_SDPISOLVER *sdpisolver)

SCIP_Bool	SCIPsdpiSolverIsPrimalInfeasible (SCIP_SDPISOLVER *sdpisolver)

SCIP_Bool	SCIPsdpiSolverIsPrimalFeasible (SCIP_SDPISOLVER *sdpisolver)

SCIP_Bool	SCIPsdpiSolverIsDualUnbounded (SCIP_SDPISOLVER *sdpisolver)

SCIP_Bool	SCIPsdpiSolverIsDualInfeasible (SCIP_SDPISOLVER *sdpisolver)

SCIP_Bool	SCIPsdpiSolverIsDualFeasible (SCIP_SDPISOLVER *sdpisolver)

SCIP_Bool	SCIPsdpiSolverIsConverged (SCIP_SDPISOLVER *sdpisolver)

SCIP_Bool	SCIPsdpiSolverIsObjlimExc (SCIP_SDPISOLVER *sdpisolver)

SCIP_Bool	SCIPsdpiSolverIsIterlimExc (SCIP_SDPISOLVER *sdpisolver)

SCIP_Bool	SCIPsdpiSolverIsTimelimExc (SCIP_SDPISOLVER *sdpisolver)

int	SCIPsdpiSolverGetInternalStatus (SCIP_SDPISOLVER *sdpisolver)

SCIP_Bool	SCIPsdpiSolverIsOptimal (SCIP_SDPISOLVER *sdpisolver)

SCIP_Bool	SCIPsdpiSolverIsAcceptable (SCIP_SDPISOLVER *sdpisolver)

SCIP_RETCODE	SCIPsdpiSolverIgnoreInstability (SCIP_SDPISOLVER sdpisolver, SCIP_Bool success)

SCIP_RETCODE	SCIPsdpiSolverGetObjval (SCIP_SDPISOLVER sdpisolver, SCIP_Real objval)

SCIP_RETCODE	SCIPsdpiSolverGetSol (SCIP_SDPISOLVER sdpisolver, SCIP_Real objval, SCIP_Real dualsol, int dualsollength)

SCIP_RETCODE	SCIPsdpiSolverGetPrimalBoundVars (SCIP_SDPISOLVER sdpisolver, SCIP_Real lbvars, SCIP_Real ubvars, int arraylength)

SCIP_RETCODE	SCIPsdpiSolverGetIterations (SCIP_SDPISOLVER sdpisolver, int iterations)

SCIP_RETCODE	SCIPsdpiSolverGetSdpCalls (SCIP_SDPISOLVER sdpisolver, int calls)

SCIP_RETCODE	SCIPsdpiSolverSettingsUsed (SCIP_SDPISOLVER sdpisolver, SCIP_SDPSOLVERSETTING usedsetting)

Numerical Methods
SCIP_Real	SCIPsdpiSolverInfinity (SCIP_SDPISOLVER *sdpisolver)

SCIP_Bool	SCIPsdpiSolverIsInfinity (SCIP_SDPISOLVER *sdpisolver, SCIP_Real val)

SCIP_RETCODE	SCIPsdpiSolverGetRealpar (SCIP_SDPISOLVER sdpisolver, SCIP_SDPPARAM type, SCIP_Real dval)

SCIP_RETCODE	SCIPsdpiSolverSetRealpar (SCIP_SDPISOLVER *sdpisolver, SCIP_SDPPARAM type, SCIP_Real dval)

SCIP_RETCODE	SCIPsdpiSolverGetIntpar (SCIP_SDPISOLVER sdpisolver, SCIP_SDPPARAM type, int ival)

SCIP_RETCODE	SCIPsdpiSolverSetIntpar (SCIP_SDPISOLVER *sdpisolver, SCIP_SDPPARAM type, int ival)

SCIP_RETCODE	SCIPsdpiSolverComputeLambdastar (SCIP_SDPISOLVER *sdpisolver, SCIP_Real maxguess)

SCIP_RETCODE	SCIPsdpiSolverComputePenaltyparam (SCIP_SDPISOLVER sdpisolver, SCIP_Real maxcoeff, SCIP_Real penaltyparam)

SCIP_RETCODE	SCIPsdpiSolverComputeMaxPenaltyparam (SCIP_SDPISOLVER sdpisolver, SCIP_Real penaltyparam, SCIP_Real maxpenaltyparam)

File Interface Methods
SCIP_RETCODE	SCIPsdpiSolverReadSDP (SCIP_SDPISOLVER sdpisolver, const char fname)

SCIP_RETCODE	SCIPsdpiSolverWriteSDP (SCIP_SDPISOLVER sdpisolver, const char fname)

Detailed Description

interface for SDPA

Author: Tristan Gally; Ambros Gleixner

Definition in file sdpisolver_sdpa.cpp.

Macro Definition Documentation

#define EPSILONCHANGE 1

change epsilon by this factor when switching from fast to default and from default to stable settings

Definition at line 62 of file sdpisolver_sdpa.cpp.

Referenced by SCIPsdpiSolverLoadAndSolveWithPenalty().

#define FEASTOLCHANGE 1

change feastol by this factor when switching from fast to default and from default to stable settings

Definition at line 63 of file sdpisolver_sdpa.cpp.

Referenced by SCIPsdpiSolverLoadAndSolveWithPenalty().

#define PENALTYBOUNDTOL 1E-3

if the relative gap between Tr(X) and penaltyparam for a primal solution of the penaltyformulation is bigger than this value, it will be reported to the sdpi

Definition at line 64 of file sdpisolver_sdpa.cpp.

Referenced by SCIPsdpiSolverLoadAndSolveWithPenalty().

#define MIN_LAMBDASTAR 1e0

if lambda star is to be computed, this is the minimum value it will take

Definition at line 68 of file sdpisolver_sdpa.cpp.

Referenced by SCIPsdpiSolverComputeLambdastar().

#define MAX_LAMBDASTAR 1e8

if lambda star is to be computed, this is the maximum value it will take

Definition at line 69 of file sdpisolver_sdpa.cpp.

Referenced by SCIPsdpiSolverComputeLambdastar().

#define LAMBDASTAR_FACTOR 1e0

if lambda star is to be computed, the biggest guess of the SDP blocks is multiplied by this value

Definition at line 70 of file sdpisolver_sdpa.cpp.

Referenced by SCIPsdpiSolverComputeLambdastar().

#define LAMBDASTAR_TWOPOINTS TRUE

if lambda star is to be computed, should we use only a low and a high value or instead a continuous interval

Definition at line 71 of file sdpisolver_sdpa.cpp.

#define LAMBDASTAR_THRESHOLD 1e1

if lambda star is to be computed and LAMBDASTAR_TWOPOINTS=TRUE, then we distinguish between low and high using this

Definition at line 72 of file sdpisolver_sdpa.cpp.

Referenced by SCIPsdpiSolverComputeLambdastar().

#define LAMBDASTAR_LOW 1.5

if lambda star is to be computed and LAMBDASTAR_TWOPOINTS=TRUE, then this is the value for below the threshold

Definition at line 73 of file sdpisolver_sdpa.cpp.

Referenced by SCIPsdpiSolverComputeLambdastar().

#define LAMBDASTAR_HIGH 1e5

if lambda star is to be computed and LAMBDASTAR_TWOPOINTS=TRUE, then this is the value for above the threshold

Definition at line 74 of file sdpisolver_sdpa.cpp.

Referenced by SCIPsdpiSolverComputeLambdastar().

#define MIN_PENALTYPARAM 1e5

if the penalty parameter is to be computed, this is the minimum value it will take

Definition at line 76 of file sdpisolver_sdpa.cpp.

Referenced by SCIPsdpiSolverComputePenaltyparam().

#define MAX_PENALTYPARAM 1e12

if the penalty parameter is to be computed, this is the maximum value it will take

Definition at line 77 of file sdpisolver_sdpa.cpp.

Referenced by SCIPsdpiSolverComputePenaltyparam().

#define PENALTYPARAM_FACTOR 1e1

if the penalty parameter is to be computed, the maximal objective coefficient will be multiplied by this

Definition at line 78 of file sdpisolver_sdpa.cpp.

Referenced by SCIPsdpiSolverComputePenaltyparam().

#define MAX_MAXPENALTYPARAM 1e15

if the maximum penaltyparameter is to be computed, this is the maximum value it will take

Definition at line 79 of file sdpisolver_sdpa.cpp.

Referenced by SCIPsdpiSolverComputeMaxPenaltyparam().

#define MAXPENALTYPARAM_FACTOR 1e6

if the maximum penaltyparameter is to be computed, it will be set to penaltyparam * this

Definition at line 80 of file sdpisolver_sdpa.cpp.

Referenced by SCIPsdpiSolverComputeMaxPenaltyparam().

#define BMS_CALL ( x )

Value:

do                                                                                     \
                      {                                                                                      \
                         if( NULL == (x) )                                                                   \
                         {                                                                                   \
                            SCIPerrorMessage("No memory in function call.\n");                               \
                            return SCIP_NOMEMORY;                                                            \
                         }                                                                                   \
                      }                                                                                      \
                      while( FALSE )

Checks if a BMSallocMemory-call was successfull, otherwise returns SCIP_NOMEMRY.

Definition at line 83 of file sdpisolver_sdpa.cpp.

Referenced by SCIPsdpiSolverCreate(), and SCIPsdpiSolverLoadAndSolveWithPenalty().

#define CHECK_IF_SOLVED ( sdpisolver )

Value:

do                                                                      \
                      {                                                                                      \
                         if (!(sdpisolver->solved))                                                          \
                         {                                                                                   \
                            SCIPerrorMessage("Tried to access solution information for SDP %d ahead of solving!\n", sdpisolver->sdpcounter);  \
                            return SCIP_LPERROR;                                                             \
                         }                                                                                   \
                      }                                                                                      \
                      while( FALSE )

This will be called in all functions that want to access solution information to check if the problem was solved since the last change of the problem.

Definition at line 94 of file sdpisolver_sdpa.cpp.

Referenced by SCIPsdpiSolverGetObjval(), SCIPsdpiSolverGetPrimalBoundVars(), SCIPsdpiSolverGetSol(), SCIPsdpiSolverGetSolFeasibility(), and SCIPsdpiSolverSettingsUsed().

#define CHECK_IF_SOLVED_BOOL ( sdpisolver )

Value:

do                                                                 \
                      {                                                                                      \
                         if (!(sdpisolver->solved))                                                          \
                         {                                                                                   \
                            SCIPerrorMessage("Tried to access solution information for SDP %d ahead of solving!\n", sdpisolver->sdpcounter);  \
                            return FALSE;                                                                    \
                         }                                                                                   \
                      }                                                                                      \
                      while( FALSE )

This is the same as CHECK_IF_SOLVED, but will be called for methods returning a bool instead of a SCIP_RETURNCODE

Definition at line 105 of file sdpisolver_sdpa.cpp.

Referenced by SCIPsdpiSolverFeasibilityKnown(), SCIPsdpiSolverIsAcceptable(), SCIPsdpiSolverIsConverged(), SCIPsdpiSolverIsDualFeasible(), SCIPsdpiSolverIsDualInfeasible(), SCIPsdpiSolverIsDualUnbounded(), SCIPsdpiSolverIsIterlimExc(), SCIPsdpiSolverIsObjlimExc(), SCIPsdpiSolverIsOptimal(), SCIPsdpiSolverIsPrimalFeasible(), SCIPsdpiSolverIsPrimalInfeasible(), and SCIPsdpiSolverIsPrimalUnbounded().

Function Documentation

static SCIP_Bool isFixed	(	SCIP_SDPISOLVER *	sdpisolver,
		SCIP_Real	lb,
		SCIP_Real	ub
	)

static

Test if a lower bound lb is not smaller than an upper bound ub, meaning that lb > ub - epsilon

Parameters

sdpisolver	pointer to an SDP-solver interface
lb	lower bound
ub	upper bound

Definition at line 156 of file sdpisolver_sdpa.cpp.

Referenced by SCIPsdpiSolverLoadAndSolveWithPenalty().

const char* SCIPsdpiSolverGetSolverName ( void )

gets name and version (if available) of SDP-solver

Definition at line 181 of file sdpisolver_sdpa.cpp.

Referenced by SCIPsdpiGetSolverName().

const char* SCIPsdpiSolverGetSolverDesc ( void )

gets description of SDP-solver (developer, webpage, ...)

Definition at line 189 of file sdpisolver_sdpa.cpp.

Referenced by SCIPsdpiGetSolverDesc().

void* SCIPsdpiSolverGetSolverPointer ( SCIP_SDPISOLVER * sdpisolver )

gets pointer to SDP-solver - use only with great care

The behavior of this function depends on the solver and its use is therefore only recommended if you really know what you are doing. In general, it returns a pointer to the SDP-solver object.

Parameters

sdpisolver pointer to an SDP-solver interface

Definition at line 202 of file sdpisolver_sdpa.cpp.

Referenced by SCIPsdpiGetSolverPointer().

SCIP_RETCODE SCIPsdpiSolverCreate	(	SCIP_SDPISOLVER **	sdpisolver,
		SCIP_MESSAGEHDLR *	messagehdlr,
		BMS_BLKMEM *	blkmem
	)

creates an SDP solver interface

Parameters

sdpisolver	pointer to an SDP-solver interface
messagehdlr	message handler to use for printing messages, or NULL
blkmem	block memory

Definition at line 221 of file sdpisolver_sdpa.cpp.

References BMS_CALL, SCIP_SDPSOLVERSETTING_UNSOLVED, and SCIPsdpiSolverInfinity().

Referenced by SCIPsdpiClone(), and SCIPsdpiCreate().

SCIP_RETCODE SCIPsdpiSolverFree ( SCIP_SDPISOLVER ** sdpisolver )

deletes an SDP solver interface

Parameters

sdpisolver pointer to an SDP-solver interface

Definition at line 264 of file sdpisolver_sdpa.cpp.

Referenced by SCIPsdpiFree().

SCIP_RETCODE SCIPsdpiSolverIncreaseCounter ( SCIP_SDPISOLVER * sdpisolver )

increases the SDP-Counter

Parameters

sdpisolver SDP-solver interface

Definition at line 294 of file sdpisolver_sdpa.cpp.

Referenced by SCIPsdpiSolve().

SCIP_RETCODE SCIPsdpiSolverResetCounter ( SCIP_SDPISOLVER * sdpisolver )

reset the SDP-Counter to zero

Parameters

sdpisolver SDP-solver interface

Definition at line 306 of file sdpisolver_sdpa.cpp.

Referenced by SCIPsdpiClear().

SCIP_RETCODE SCIPsdpiSolverLoadAndSolve	(	SCIP_SDPISOLVER *	sdpisolver,
		int	nvars,
		SCIP_Real *	obj,
		SCIP_Real *	lb,
		SCIP_Real *	ub,
		int	nsdpblocks,
		int *	sdpblocksizes,
		int *	sdpnblockvars,
		int	sdpconstnnonz,
		int *	sdpconstnblocknonz,
		int **	sdpconstrow,
		int **	sdpconstcol,
		SCIP_Real **	sdpconstval,
		int	sdpnnonz,
		int **	sdpnblockvarnonz,
		int **	sdpvar,
		int ***	sdprow,
		int ***	sdpcol,
		SCIP_Real ***	sdpval,
		int **	indchanges,
		int *	nremovedinds,
		int *	blockindchanges,
		int	nremovedblocks,
		int	nlpcons,
		int	noldlpcons,
		SCIP_Real *	lplhs,
		SCIP_Real *	lprhs,
		int *	lprownactivevars,
		int	lpnnonz,
		int *	lprow,
		int *	lpcol,
		SCIP_Real *	lpval,
		SCIP_Real *	start,
		SCIP_SDPSOLVERSETTING	startsettings,
		SCIP_Real	timelimit
	)

loads and solves an SDP

For the non-constant SDP- and the LP-part, the original arrays before fixings should be given, for the constant SDP-part the arrays AFTER fixings should be given. In addition, an array needs to be given, that for every block and every row/col index within that block either has value -1, meaning that this index should be deleted, or a non-negative integer stating the number of indices before it that are to be deleated, meaning that this index will be decreased by that number, in addition to that the total number of deleted indices for each block should be given. Optionally an array start may be given with a starting point for the solver (if this is NULL then the solver should start from scratch).

Warning: Depending on the solver, the given lp arrays might get sorted in their original position.

Parameters

sdpisolver	SDP-solver interface
nvars	number of variables
obj	objective coefficients of variables
lb	lower bounds of variables
ub	upper bounds of variables
nsdpblocks	number of SDP-blocks
sdpblocksizes	sizes of the SDP-blocks (may be NULL if nsdpblocks = sdpconstnnonz = sdpnnonz = 0)
sdpnblockvars	number of variables that exist in each block
sdpconstnnonz	number of nonzero elements in the constant matrices of the SDP-blocks AFTER FIXINGS
sdpconstnblocknonz	number of nonzeros for each variable in the constant part, also the i-th entry gives the number of entries of sdpconst row/col/val [i] AFTER FIXINGS
sdpconstrow	pointers to row-indices for each block AFTER FIXINGS
sdpconstcol	pointers to column-indices for each block AFTER FIXINGS
sdpconstval	pointers to the values of the nonzeros for each block AFTER FIXINGS
sdpnnonz	number of nonzero elements in the SDP-constraint-matrix
sdpnblockvarnonz	entry [i][j] gives the number of nonzeros for block i and variable j, this is exactly the number of entries of sdp row/col/val [i][j]
sdpvar	sdpvar[i][j] gives the sdp-index of the j-th variable (according to the sorting for row/col/val) in the i-th block
sdprow	pointer to the row-indices for each block and variable
sdpcol	pointer to the column-indices for each block and variable
sdpval	values of SDP-constraint-matrix entries (may be NULL if sdpnnonz = 0)
indchanges	changes needed to be done to the indices, if indchanges[block][nonz]=-1, then the index can be removed, otherwise it gives the number of indices removed before this
nremovedinds	the number of rows/cols to be fixed for each block
blockindchanges	block indizes will be modified by these, see indchanges
nremovedblocks	number of empty blocks that should be removed
nlpcons	number of active (at least two nonzeros) LP-constraints
noldlpcons	number of LP-constraints including those with less than two active nonzeros
lplhs	left-hand sides of active LP-rows after fixings (may be NULL if nlpcons = 0)
lprhs	right-hand sides of active LP-rows after fixings (may be NULL if nlpcons = 0)
lprownactivevars	number of active variables for each LP-constraint
lpnnonz	number of nonzero elements in the LP-constraint-matrix
lprow	row-index for each entry in lpval-array, might get sorted (may be NULL if lpnnonz = 0)
lpcol	column-index for each entry in lpval-array, might get sorted (may be NULL if lpnnonz = 0)
lpval	values of LP-constraint-matrix entries, might get sorted (may be NULL if lpnnonz = 0)
start	NULL or a starting point for the solver, this should have length nvars
startsettings	settings used to start with in SDPA, currently not used for DSDP, set this to SCIP_SDPSOLVERSETTING_UNSOLVED to ignore it and start from scratch
timelimit	after this many seconds solving will be aborted (currently only implemented for DSDP)

Definition at line 340 of file sdpisolver_sdpa.cpp.

References SCIPsdpiSolverLoadAndSolveWithPenalty().

Referenced by checkSlaterCondition(), and SCIPsdpiSolve().

SCIP_RETCODE SCIPsdpiSolverLoadAndSolveWithPenalty	(	SCIP_SDPISOLVER *	sdpisolver,
		SCIP_Real	penaltyparam,
		SCIP_Bool	withobj,
		SCIP_Bool	rbound,
		int	nvars,
		SCIP_Real *	obj,
		SCIP_Real *	lb,
		SCIP_Real *	ub,
		int	nsdpblocks,
		int *	sdpblocksizes,
		int *	sdpnblockvars,
		int	sdpconstnnonz,
		int *	sdpconstnblocknonz,
		int **	sdpconstrow,
		int **	sdpconstcol,
		SCIP_Real **	sdpconstval,
		int	sdpnnonz,
		int **	sdpnblockvarnonz,
		int **	sdpvar,
		int ***	sdprow,
		int ***	sdpcol,
		SCIP_Real ***	sdpval,
		int **	indchanges,
		int *	nremovedinds,
		int *	blockindchanges,
		int	nremovedblocks,
		int	nlpcons,
		int	noldlpcons,
		SCIP_Real *	lplhs,
		SCIP_Real *	lprhs,
		int *	rownactivevars,
		int	lpnnonz,
		int *	lprow,
		int *	lpcol,
		SCIP_Real *	lpval,
		SCIP_Real *	start,
		SCIP_SDPSOLVERSETTING	startsettings,
		SCIP_Real	timelimit,
		SCIP_Bool *	feasorig,
		SCIP_Bool *	penaltybound
	)

loads and solves an SDP using a penalty formulation

The penalty formulation of the SDP is:

$\begin{eqnarray*} \min & & b^T y + \Gamma r \\ \mbox{s.t.} & & \sum_{j=1}^n A_j^i y_j - A_0^i + r \cdot \mathbb{I} \succeq 0 \quad \forall i \leq m \\ & & Dy + r \cdot \mathbb{I} \geq d \\ & & l \leq y \leq u \\ & & r \geq 0.\end{eqnarray*}$

Alternatively withobj can be set to false to set b to 0 and only check for feasibility (if the optimal objective value is bigger than 0 the problem is infeasible, otherwise it's feasible), and rbound can be set to false to remove the non-negativity condition on r. For the non-constant SDP- and the LP-part the original arrays before fixings should be given, for the constant SDP-part the arrays AFTER fixings should be given. In addition, an array needs to be given, that for every block and every row/col index within that block either has value -1, meaning that this index should be deleted, or a non-negative integer stating the number of indices before it that are to be deleated, meaning that this index will be decreased by that number. Moreover, the total number of deleted indices for each block should be given. An optional starting point for the solver may be given; if it is NULL, the solver will start from scratch.

Warning: Depending on the solver, the given lp arrays might get sorted in their original position.

Parameters

sdpisolver	SDP-solver interface
penaltyparam	the Gamma above, needs to be >= 0
withobj	if this is false the objective is set to 0
rbound	should r be non-negative ?
nvars	number of variables
obj	objective coefficients of variables
lb	lower bounds of variables
ub	upper bounds of variables
nsdpblocks	number of SDP-blocks
sdpblocksizes	sizes of the SDP-blocks (may be NULL if nsdpblocks = sdpconstnnonz = sdpnnonz = 0)
sdpnblockvars	number of variables that exist in each block
sdpconstnnonz	number of nonzero elements in the constant matrices of the SDP-blocks AFTER FIXINGS
sdpconstnblocknonz	number of nonzeros for each variable in the constant part, also the i-th entry gives the number of entries of sdpconst row/col/val [i] AFTER FIXINGS
sdpconstrow	pointers to row-indices for each block AFTER FIXINGS
sdpconstcol	pointers to column-indices for each block AFTER FIXINGS
sdpconstval	pointers to the values of the nonzeros for each block AFTER FIXINGS
sdpnnonz	number of nonzero elements in the SDP-constraint-matrix
sdpnblockvarnonz	entry [i][j] gives the number of nonzeros for block i and variable j, this is exactly the number of entries of sdp row/col/val [i][j]
sdpvar	sdpvar[i][j] gives the sdp-index of the j-th variable (according to the sorting for row/col/val) in the i-th block
sdprow	pointer to the row-indices for each block and variable
sdpcol	pointer to the column-indices for each block and variable
sdpval	values of SDP-constraint-matrix entries (may be NULL if sdpnnonz = 0)
indchanges	changes needed to be done to the indices, if indchanges[block][nonz]=-1, then the index can be removed, otherwise it gives the number of indices removed before this
nremovedinds	the number of rows/cols to be fixed for each block
blockindchanges	block indizes will be modified by these, see indchanges
nremovedblocks	number of empty blocks that should be removed
nlpcons	number of active (at least two nonzeros) LP-constraints
noldlpcons	number of LP-constraints including those with less than two active nonzeros
lplhs	left-hand sides of active LP-rows after fixings (may be NULL if nlpcons = 0)
lprhs	right-hand sides of active LP-rows after fixings (may be NULL if nlpcons = 0)
rownactivevars	number of active variables for each LP-constraint
lpnnonz	number of nonzero elements in the LP-constraint-matrix
lprow	row-index for each entry in lpval-array, might get sorted (may be NULL if lpnnonz = 0)
lpcol	column-index for each entry in lpval-array, might get sorted (may be NULL if lpnnonz = 0)
lpval	values of LP-constraint-matrix entries, might get sorted (may be NULL if lpnnonz = 0)
start	NULL or a starting point for the solver, this should have length nvars
startsettings	settings used to start with in SDPA, currently not used for DSDP, set this to SCIP_SDPSOLVERSETTING_UNSOLVED to ignore it and start from scratch
timelimit	after this many seconds solving will be aborted (currently only implemented for DSDP)
feasorig	pointer to store if the solution to the penalty-formulation is feasible for the original problem (may be NULL if penaltyparam = 0)
penaltybound	pointer to store if the primal solution reached the bound Tr(X) <= penaltyparam in the primal problem, this is also an indication of the penalty parameter being to small (may be NULL if not needed)

Definition at line 408 of file sdpisolver_sdpa.cpp.

References BMS_CALL, EPSILONCHANGE, FEASTOLCHANGE, isFixed(), PENALTYBOUNDTOL, SCIP_SDPSOLVERSETTING_FAST, SCIP_SDPSOLVERSETTING_MEDIUM, SCIP_SDPSOLVERSETTING_PENALTY, SCIP_SDPSOLVERSETTING_STABLE, SCIP_SDPSOLVERSETTING_UNSOLVED, SCIPsdpiSolverInfinity(), SCIPsdpiSolverIsAcceptable(), and SCIPsdpiSolverIsInfinity().

Referenced by checkSlaterCondition(), SCIPsdpiSolve(), and SCIPsdpiSolverLoadAndSolve().

SCIP_Bool SCIPsdpiSolverWasSolved ( SCIP_SDPISOLVER * sdpisolver )

returns whether a solve method was called after the last modification of the SDP

Parameters

sdpisolver pointer to SDP-solver interface

Definition at line 1371 of file sdpisolver_sdpa.cpp.

Referenced by SCIPsdpiSolve().

SCIP_Bool SCIPsdpiSolverFeasibilityKnown ( SCIP_SDPISOLVER * sdpisolver )

returns true if the solver could determine whether the problem is feasible

So it returns true if the solver knows that the problem is feasible/infeasible/unbounded, it returns false if the solver does not know anything about the feasibility status and thus the functions IsPrimalFeasible etc. should not be used.

Parameters

sdpisolver pointer to SDP-solver interface

Definition at line 1385 of file sdpisolver_sdpa.cpp.

References CHECK_IF_SOLVED_BOOL.

Referenced by SCIPsdpiFeasibilityKnown().

SCIP_RETCODE SCIPsdpiSolverGetSolFeasibility	(	SCIP_SDPISOLVER *	sdpisolver,
		SCIP_Bool *	primalfeasible,
		SCIP_Bool *	dualfeasible
	)

gets information about primal and dual feasibility of the current SDP solution

Parameters

sdpisolver	pointer to an SDP-solver interface
primalfeasible	stores primal feasibility status
dualfeasible	stores dual feasibility status

Definition at line 1404 of file sdpisolver_sdpa.cpp.

References CHECK_IF_SOLVED.

Referenced by SCIPsdpiGetSolFeasibility().

SCIP_Bool SCIPsdpiSolverIsPrimalUnbounded ( SCIP_SDPISOLVER * sdpisolver )

returns TRUE iff SDP is proven to be primal unbounded, returns FALSE with a debug-message if the solver could not determine feasibility

Parameters

sdpisolver pointer to SDP-solver interface

Definition at line 1458 of file sdpisolver_sdpa.cpp.

References CHECK_IF_SOLVED_BOOL.

Referenced by checkSlaterCondition(), and SCIPsdpiIsPrimalUnbounded().

SCIP_Bool SCIPsdpiSolverIsPrimalInfeasible ( SCIP_SDPISOLVER * sdpisolver )

returns TRUE iff SDP is proven to be primal infeasible, returns FALSE with a debug-message if the solver could not determine feasibility

Parameters

sdpisolver pointer to SDP-solver interface

Definition at line 1488 of file sdpisolver_sdpa.cpp.

References CHECK_IF_SOLVED_BOOL.

Referenced by SCIPsdpiIsPrimalInfeasible().

SCIP_Bool SCIPsdpiSolverIsPrimalFeasible ( SCIP_SDPISOLVER * sdpisolver )

returns TRUE iff SDP is proven to be primal feasible, returns FALSE with a debug-message if the solver could not determine feasibility

Parameters

sdpisolver pointer to SDP-solver interface

Definition at line 1518 of file sdpisolver_sdpa.cpp.

References CHECK_IF_SOLVED_BOOL.

Referenced by SCIPsdpiIsPrimalFeasible().

SCIP_Bool SCIPsdpiSolverIsDualUnbounded ( SCIP_SDPISOLVER * sdpisolver )

returns TRUE iff SDP is proven to be dual unbounded, returns FALSE with a debug-message if the solver could not determine feasibility

Parameters

sdpisolver pointer to SDP-solver interface

Definition at line 1548 of file sdpisolver_sdpa.cpp.

References CHECK_IF_SOLVED_BOOL.

Referenced by checkSlaterCondition(), and SCIPsdpiIsDualUnbounded().

SCIP_Bool SCIPsdpiSolverIsDualInfeasible ( SCIP_SDPISOLVER * sdpisolver )

returns TRUE iff SDP is proven to be dual infeasible, returns FALSE with a debug-message if the solver could not determine feasibility

Parameters

sdpisolver pointer to SDP-solver interface

Definition at line 1578 of file sdpisolver_sdpa.cpp.

References CHECK_IF_SOLVED_BOOL.

Referenced by checkSlaterCondition(), SCIPsdpiIsDualInfeasible(), and SCIPsdpiSolve().

SCIP_Bool SCIPsdpiSolverIsDualFeasible ( SCIP_SDPISOLVER * sdpisolver )

returns TRUE iff SDP is proven to be dual feasible, returns FALSE with a debug-message if the solver could not determine feasibility

Parameters

sdpisolver pointer to SDP-solver interface

Definition at line 1608 of file sdpisolver_sdpa.cpp.

References CHECK_IF_SOLVED_BOOL.

Referenced by SCIPsdpiIsDualFeasible().

SCIP_Bool SCIPsdpiSolverIsConverged ( SCIP_SDPISOLVER * sdpisolver )

returns TRUE iff the solver converged

Parameters

sdpisolver pointer to SDP-solver interface

Definition at line 1637 of file sdpisolver_sdpa.cpp.

References CHECK_IF_SOLVED_BOOL.

Referenced by SCIPsdpiIsConverged(), and SCIPsdpiSolverIsAcceptable().

SCIP_Bool SCIPsdpiSolverIsObjlimExc ( SCIP_SDPISOLVER * sdpisolver )

returns TRUE iff the objective limit was reached

Parameters

sdpisolver pointer to SDP-solver interface

Definition at line 1656 of file sdpisolver_sdpa.cpp.

References CHECK_IF_SOLVED_BOOL.

Referenced by SCIPsdpiIsObjlimExc().

SCIP_Bool SCIPsdpiSolverIsIterlimExc ( SCIP_SDPISOLVER * sdpisolver )

returns TRUE iff the iteration limit was reached

Parameters

sdpisolver pointer to SDP-solver interface

Definition at line 1675 of file sdpisolver_sdpa.cpp.

References CHECK_IF_SOLVED_BOOL.

Referenced by SCIPsdpiIsIterlimExc().

SCIP_Bool SCIPsdpiSolverIsTimelimExc ( SCIP_SDPISOLVER * sdpisolver )

returns TRUE iff the time limit was reached

Parameters

sdpisolver pointer to SDP-solver interface

Definition at line 1697 of file sdpisolver_sdpa.cpp.

Referenced by SCIPsdpiIsTimelimExc(), and SCIPsdpiSolve().

int SCIPsdpiSolverGetInternalStatus ( SCIP_SDPISOLVER * sdpisolver )

returns the internal solution status of the solver, which has the following meaning:
-1: solver was not started
0: converged
1: infeasible start
2: numerical problems
3: objective limit reached
4: iteration limit reached
5: time limit reached
6: user termination
7: other

Parameters

sdpisolver pointer to SDP-solver interface

Definition at line 1716 of file sdpisolver_sdpa.cpp.

Referenced by SCIPsdpiGetInternalStatus().

SCIP_Bool SCIPsdpiSolverIsOptimal ( SCIP_SDPISOLVER * sdpisolver )

returns TRUE iff SDP was solved to optimality, meaning the solver converged and returned primal and dual feasible solutions

Parameters

sdpisolver pointer to SDP-solver interface

Definition at line 1743 of file sdpisolver_sdpa.cpp.

References CHECK_IF_SOLVED_BOOL.

Referenced by checkSlaterCondition(), SCIPsdpiIsOptimal(), and SCIPsdpiSolve().

SCIP_Bool SCIPsdpiSolverIsAcceptable ( SCIP_SDPISOLVER * sdpisolver )

returns TRUE iff SDP was solved to optimality or some other status was reached that is still acceptable inside a Branch & Bound framework

Parameters

sdpisolver pointer to SDP-solver interface

Definition at line 1763 of file sdpisolver_sdpa.cpp.

References CHECK_IF_SOLVED_BOOL, and SCIPsdpiSolverIsConverged().

Referenced by SCIPsdpiIsAcceptable(), SCIPsdpiSolve(), and SCIPsdpiSolverLoadAndSolveWithPenalty().

SCIP_RETCODE SCIPsdpiSolverIgnoreInstability	(	SCIP_SDPISOLVER *	sdpisolver,
		SCIP_Bool *	success
	)

tries to reset the internal status of the SDP-solver in order to ignore an instability of the last solving call

Parameters

sdpisolver	pointer to an SDP-solver interface
success	pointer to store, whether the instability could be ignored

Definition at line 1788 of file sdpisolver_sdpa.cpp.

SCIP_RETCODE SCIPsdpiSolverGetObjval	(	SCIP_SDPISOLVER *	sdpisolver,
		SCIP_Real *	objval
	)

gets objective value of solution

Parameters

sdpisolver	pointer to an SDP-solver interface
objval	pointer to store the objective value

Definition at line 1799 of file sdpisolver_sdpa.cpp.

References CHECK_IF_SOLVED.

Referenced by checkSlaterCondition(), SCIPsdpiGetLowerObjbound(), SCIPsdpiGetObjval(), and SCIPsdpiSolve().

SCIP_RETCODE SCIPsdpiSolverGetSol	(	SCIP_SDPISOLVER *	sdpisolver,
		SCIP_Real *	objval,
		SCIP_Real *	dualsol,
		int *	dualsollength
	)

gets dual solution vector for feasible SDPs

If dualsollength isn't equal to the number of variables this will return the needed length and a debug message is thrown.

Parameters

sdpisolver	pointer to an SDP-solver interface
objval	pointer to store the objective value, may be NULL if not needed
dualsol	pointer to store the dual solution vector, may be NULL if not needed
dualsollength	length of the dual sol vector, must be 0 if dualsol is NULL, if this is less than the number of variables in the SDP, a DebugMessage will be thrown and this is set to the needed value

Definition at line 1829 of file sdpisolver_sdpa.cpp.

References CHECK_IF_SOLVED.

Referenced by SCIPsdpiGetSol().

SCIP_RETCODE SCIPsdpiSolverGetPrimalBoundVars	(	SCIP_SDPISOLVER *	sdpisolver,
		SCIP_Real *	lbvars,
		SCIP_Real *	ubvars,
		int *	arraylength
	)

gets the primal variables corresponding to the lower and upper variable-bounds in the dual problem

The last input should specify the length of the arrays. If this is less than the number of variables, the needed length will be returned and a debug message thrown.

Note: If a variable is either fixed or unbounded in the dual problem, a zero will be returned for the non-existent primal variable.

Parameters

sdpisolver	pointer to an SDP-solver interface
lbvars	pointer to store the values of the variables corresponding to lower bounds in the dual problems
ubvars	pointer to store the values of the variables corresponding to upper bounds in the dual problems
arraylength	input: length of lbvars and ubvars output: number of elements inserted into lbvars/ubvars (or needed length if it wasn't sufficient)

Definition at line 1904 of file sdpisolver_sdpa.cpp.

References CHECK_IF_SOLVED.

Referenced by SCIPsdpiGetPrimalBoundVars().

SCIP_RETCODE SCIPsdpiSolverGetIterations	(	SCIP_SDPISOLVER *	sdpisolver,
		int *	iterations
	)

gets the number of SDP iterations of the last solve call

Parameters

sdpisolver	pointer to an SDP-solver interface
iterations	pointer to store the number of iterations of the last solve call

Definition at line 1978 of file sdpisolver_sdpa.cpp.

Referenced by SCIPsdpiSolve().

SCIP_RETCODE SCIPsdpiSolverGetSdpCalls	(	SCIP_SDPISOLVER *	sdpisolver,
		int *	calls
	)

gets the number of calls to the SDP-solver for the last solve call

Parameters

sdpisolver	SDP-solver interface
calls	pointer to store the number of calls to the SDP-solver for the last solve call

Definition at line 1993 of file sdpisolver_sdpa.cpp.

Referenced by SCIPsdpiSolve().

SCIP_RETCODE SCIPsdpiSolverSettingsUsed	(	SCIP_SDPISOLVER *	sdpisolver,
		SCIP_SDPSOLVERSETTING *	usedsetting
	)

gets the settings used by the SDP solver for the last solve call

Parameters

sdpisolver	SDP-solver interface
usedsetting	the setting used by the SDP-solver

Definition at line 2008 of file sdpisolver_sdpa.cpp.

References CHECK_IF_SOLVED.

Referenced by SCIPsdpiSettingsUsed(), and SCIPsdpiSlaterSettings().

SCIP_Real SCIPsdpiSolverInfinity ( SCIP_SDPISOLVER * sdpisolver )

returns value treated as infinity in the SDP-solver

Parameters

sdpisolver pointer to an SDP-solver interface

Definition at line 2035 of file sdpisolver_sdpa.cpp.

Referenced by checkSlaterCondition(), SCIPsdpiCreate(), SCIPsdpiInfinity(), SCIPsdpiSlaterSettings(), SCIPsdpiSolve(), SCIPsdpiSolverCreate(), SCIPsdpiSolverIsInfinity(), and SCIPsdpiSolverLoadAndSolveWithPenalty().

SCIP_Bool SCIPsdpiSolverIsInfinity	(	SCIP_SDPISOLVER *	sdpisolver,
		SCIP_Real	val
	)

checks if given value is treated as (plus or minus) infinity in the SDP-solver

Parameters

sdpisolver	pointer to an SDP-solver interface
val	value to be checked for infinity

Definition at line 2043 of file sdpisolver_sdpa.cpp.

References SCIPsdpiSolverInfinity().

Referenced by checkSlaterCondition(), and SCIPsdpiSolverLoadAndSolveWithPenalty().

SCIP_RETCODE SCIPsdpiSolverGetRealpar	(	SCIP_SDPISOLVER *	sdpisolver,
		SCIP_SDPPARAM	type,
		SCIP_Real *	dval
	)

gets floating point parameter of SDP-Solver

Parameters

sdpisolver	pointer to an SDP-solver interface
type	parameter number
dval	buffer to store the parameter value

Definition at line 2052 of file sdpisolver_sdpa.cpp.

References SCIP_SDPPAR_EPSILON, SCIP_SDPPAR_FEASTOL, SCIP_SDPPAR_LAMBDASTAR, SCIP_SDPPAR_OBJLIMIT, and SCIP_SDPPAR_PENALTYPARAM.

Referenced by SCIPsdpiGetRealpar().

SCIP_RETCODE SCIPsdpiSolverSetRealpar	(	SCIP_SDPISOLVER *	sdpisolver,
		SCIP_SDPPARAM	type,
		SCIP_Real	dval
	)

sets floating point parameter of SDP-Solver

Parameters

sdpisolver	pointer to an SDP-solver interface
type	parameter number
dval	parameter value

Definition at line 2087 of file sdpisolver_sdpa.cpp.

References SCIP_SDPPAR_EPSILON, SCIP_SDPPAR_FEASTOL, SCIP_SDPPAR_LAMBDASTAR, SCIP_SDPPAR_OBJLIMIT, and SCIP_SDPPAR_PENALTYPARAM.

Referenced by SCIPsdpiSetRealpar(), and SCIPsdpiSolve().

SCIP_RETCODE SCIPsdpiSolverGetIntpar	(	SCIP_SDPISOLVER *	sdpisolver,
		SCIP_SDPPARAM	type,
		int *	ival
	)

gets integer parameter of SDP-Solver

Parameters

sdpisolver	pointer to an SDP-solver interface
type	parameter number
ival	parameter value

Definition at line 2124 of file sdpisolver_sdpa.cpp.

References SCIP_SDPPAR_SDPINFO.

Referenced by SCIPsdpiGetIntpar(), and SCIPsdpiSetIntpar().

SCIP_RETCODE SCIPsdpiSolverSetIntpar	(	SCIP_SDPISOLVER *	sdpisolver,
		SCIP_SDPPARAM	type,
		int	ival
	)

sets integer parameter of SDP-Solver

Parameters

sdpisolver	pointer to an SDP-solver interface
type	parameter number
ival	parameter value

Definition at line 2146 of file sdpisolver_sdpa.cpp.

References SCIP_SDPPAR_SDPINFO.

Referenced by SCIPsdpiSetIntpar().

SCIP_RETCODE SCIPsdpiSolverComputeLambdastar	(	SCIP_SDPISOLVER *	sdpisolver,
		SCIP_Real	maxguess
	)

compute and set lambdastar (only used for SDPA)

Parameters

sdpisolver	pointer to an SDP-solver interface
maxguess	maximum guess for lambda star of all SDP-constraints

Definition at line 2168 of file sdpisolver_sdpa.cpp.

References LAMBDASTAR_FACTOR, LAMBDASTAR_HIGH, LAMBDASTAR_LOW, LAMBDASTAR_THRESHOLD, MAX_LAMBDASTAR, and MIN_LAMBDASTAR.

Referenced by SCIPsdpiComputeLambdastar().

SCIP_RETCODE SCIPsdpiSolverComputePenaltyparam	(	SCIP_SDPISOLVER *	sdpisolver,
		SCIP_Real	maxcoeff,
		SCIP_Real *	penaltyparam
	)

compute and set the penalty parameter

Parameters

sdpisolver	pointer to an SDP-solver interface
maxcoeff	maximum objective coefficient
penaltyparam	the computed penalty parameter

Definition at line 2209 of file sdpisolver_sdpa.cpp.

References MAX_PENALTYPARAM, MIN_PENALTYPARAM, and PENALTYPARAM_FACTOR.

Referenced by SCIPsdpiComputePenaltyparam().

SCIP_RETCODE SCIPsdpiSolverComputeMaxPenaltyparam	(	SCIP_SDPISOLVER *	sdpisolver,
		SCIP_Real	penaltyparam,
		SCIP_Real *	maxpenaltyparam
	)

compute and set the maximum penalty parameter

Parameters

sdpisolver	pointer to an SDP-solver interface
penaltyparam	the initial penalty parameter
maxpenaltyparam	the computed maximum penalty parameter

Definition at line 2241 of file sdpisolver_sdpa.cpp.

References MAX_MAXPENALTYPARAM, and MAXPENALTYPARAM_FACTOR.

Referenced by SCIPsdpiComputeMaxPenaltyparam().

SCIP_RETCODE SCIPsdpiSolverReadSDP	(	SCIP_SDPISOLVER *	sdpisolver,
		const char *	fname
	)

reads SDP from a file

Parameters

sdpisolver	pointer to an SDP-solver interface
fname	file name

Definition at line 2281 of file sdpisolver_sdpa.cpp.

SCIP_RETCODE SCIPsdpiSolverWriteSDP	(	SCIP_SDPISOLVER *	sdpisolver,
		const char *	fname
	)

writes SDP to a file

Parameters

sdpisolver	pointer to an SDP-solver interface
fname	file name

Definition at line 2291 of file sdpisolver_sdpa.cpp.

Macros

Functions

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Macro Definition Documentation

Function Documentation