SCIP
Solving Constraint Integer Programs
nlhdlr_perspective.c File Reference
Detailed Description
perspective nonlinear handler
Definition in file nlhdlr_perspective.c.
#include <string.h>#include "scip/nlhdlr_perspective.h"#include "scip/cons_nonlinear.h"#include "scip/scip_sol.h"#include "scip/pub_misc_rowprep.h"#include "scip/nlhdlr.h"Go to the source code of this file.
Data Structures | |
| struct | SCVarData |
Macros | |
| #define | NLHDLR_NAME "perspective" |
| #define | NLHDLR_DESC "perspective handler for expressions" |
| #define | NLHDLR_DETECTPRIORITY -20 |
| #define | NLHDLR_ENFOPRIORITY 125 |
| #define | DEFAULT_MAXPROPROUNDS 1 |
| #define | DEFAULT_MINDOMREDUCTION 0.1 |
| #define | DEFAULT_MINVIOLPROBING 1e-05 |
| #define | DEFAULT_PROBINGONLYINSEPA TRUE |
| #define | DEFAULT_PROBINGFREQ 1 |
| #define | DEFAULT_CONVEXONLY FALSE |
| #define | DEFAULT_TIGHTENBOUNDS TRUE |
| #define | DEFAULT_ADJREFPOINT TRUE |
Typedefs | |
| typedef struct SCVarData | SCVARDATA |
Functions | |
| static SCIP_RETCODE | freeNlhdlrExprData (SCIP *scip, SCIP_NLHDLREXPRDATA *nlhdlrexprdata) |
| static SCIP_RETCODE | removeIndicator (SCIP *scip, SCIP_NLHDLREXPRDATA *nlexprdata, int pos) |
| static SCIP_RETCODE | addAuxVar (SCIP *scip, SCIP_NLHDLREXPRDATA *nlhdlrexprdata, SCIP_HASHMAP *auxvarmap, SCIP_VAR *auxvar) |
| static SCIP_RETCODE | addSCVarIndicator (SCIP *scip, SCVARDATA *scvdata, SCIP_VAR *indicator, SCIP_Real val0, SCIP_Real lb1, SCIP_Real ub1) |
| static SCVARDATA * | getSCVarDataInd (SCIP_HASHMAP *scvars, SCIP_VAR *var, SCIP_VAR *indicator, int *pos) |
| static SCIP_RETCODE | varIsSemicontinuous (SCIP *scip, SCIP_VAR *var, SCIP_HASHMAP *scvars, SCIP_Bool *result) |
| static SCIP_RETCODE | exprIsSemicontinuous (SCIP *scip, SCIP_NLHDLRDATA *nlhdlrdata, SCIP_NLHDLREXPRDATA *nlhdlrexprdata, SCIP_EXPR *expr, SCIP_Bool *res) |
| static SCIP_RETCODE | computeOffValues (SCIP *scip, SCIP_NLHDLRDATA *nlhdlrdata, SCIP_NLHDLREXPRDATA *nlhdlrexprdata, SCIP_EXPR *expr) |
| static SCIP_RETCODE | startProbing (SCIP *scip, SCIP_NLHDLRDATA *nlhdlrdata, SCIP_NLHDLREXPRDATA *nlhdlrexprdata, SCIP_VAR *indicator, SCIP_VAR **probingvars, SCIP_INTERVAL *probingdoms, int nprobingvars, SCIP_SOL *sol, SCIP_SOL **solcopy, SCIP_Bool *cutoff_probing) |
| static SCIP_RETCODE | analyseVarOnoffBounds (SCIP *scip, SCIP_NLHDLRDATA *nlhdlrdata, SCIP_VAR *var, SCIP_VAR *indicator, SCIP_Bool indvalue, SCIP_Bool *infeas, SCIP_Real *probinglb, SCIP_Real *probingub, SCIP_Bool doprobing, SCIP_Bool *reduceddom) |
| static SCIP_RETCODE | analyseOnoffBounds (SCIP *scip, SCIP_NLHDLRDATA *nlhdlrdata, SCIP_NLHDLREXPRDATA *nlhdlrexprdata, SCIP_VAR *indicator, SCIP_VAR ***probingvars, SCIP_INTERVAL **probingdoms, int *nprobingvars, SCIP_Bool *doprobing, SCIP_RESULT *result) |
| static SCIP_RETCODE | tightenOnBounds (SCIP_NLHDLREXPRDATA *nlhdlrexprdata, SCIP_HASHMAP *scvars, SCIP_VAR *indicator) |
| static | SCIP_DECL_NLHDLRCOPYHDLR (nlhdlrCopyhdlrPerspective) |
| static | SCIP_DECL_NLHDLRFREEHDLRDATA (nlhdlrFreehdlrdataPerspective) |
| static | SCIP_DECL_NLHDLRFREEEXPRDATA (nlhdlrFreeExprDataPerspective) |
| static | SCIP_DECL_NLHDLREXIT (nlhdlrExitPerspective) |
| static | SCIP_DECL_NLHDLRDETECT (nlhdlrDetectPerspective) |
| static | SCIP_DECL_NLHDLREVALAUX (nlhdlrEvalauxPerspective) |
| static | SCIP_DECL_NLHDLRINITSEPA (nlhdlrInitSepaPerspective) |
| static | SCIP_DECL_NLHDLRENFO (nlhdlrEnfoPerspective) |
| SCIP_RETCODE | SCIPincludeNlhdlrPerspective (SCIP *scip) |
Macro Definition Documentation
◆ NLHDLR_NAME
| #define NLHDLR_NAME "perspective" |
Definition at line 40 of file nlhdlr_perspective.c.
◆ NLHDLR_DESC
| #define NLHDLR_DESC "perspective handler for expressions" |
Definition at line 41 of file nlhdlr_perspective.c.
◆ NLHDLR_DETECTPRIORITY
| #define NLHDLR_DETECTPRIORITY -20 |
detect last so that to make use of what other handlers detected
Definition at line 42 of file nlhdlr_perspective.c.
◆ NLHDLR_ENFOPRIORITY
| #define NLHDLR_ENFOPRIORITY 125 |
enforce first because perspective cuts are always stronger
Definition at line 43 of file nlhdlr_perspective.c.
◆ DEFAULT_MAXPROPROUNDS
| #define DEFAULT_MAXPROPROUNDS 1 |
maximal number of propagation rounds in probing
Definition at line 45 of file nlhdlr_perspective.c.
◆ DEFAULT_MINDOMREDUCTION
| #define DEFAULT_MINDOMREDUCTION 0.1 |
minimal relative reduction in a variable's domain for applying probing
Definition at line 46 of file nlhdlr_perspective.c.
◆ DEFAULT_MINVIOLPROBING
| #define DEFAULT_MINVIOLPROBING 1e-05 |
minimal violation w.r.t. auxiliary variables for applying probing
Definition at line 47 of file nlhdlr_perspective.c.
◆ DEFAULT_PROBINGONLYINSEPA
| #define DEFAULT_PROBINGONLYINSEPA TRUE |
whether to do probing only in separation loop
Definition at line 48 of file nlhdlr_perspective.c.
◆ DEFAULT_PROBINGFREQ
| #define DEFAULT_PROBINGFREQ 1 |
probing frequency (-1 - no probing, 0 - root node only)
Definition at line 49 of file nlhdlr_perspective.c.
◆ DEFAULT_CONVEXONLY
| #define DEFAULT_CONVEXONLY FALSE |
whether perspective cuts are added only for convex expressions
Definition at line 50 of file nlhdlr_perspective.c.
◆ DEFAULT_TIGHTENBOUNDS
| #define DEFAULT_TIGHTENBOUNDS TRUE |
whether variable semicontinuity is used to tighten variable bounds
Definition at line 51 of file nlhdlr_perspective.c.
◆ DEFAULT_ADJREFPOINT
| #define DEFAULT_ADJREFPOINT TRUE |
whether to adjust the reference point if indicator is not 1
Definition at line 52 of file nlhdlr_perspective.c.
Typedef Documentation
◆ SCVARDATA
Definition at line 74 of file nlhdlr_perspective.c.
Function Documentation
◆ freeNlhdlrExprData()
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static |
frees nlhdlrexprdata structure
- Parameters
-
scip SCIP data structure nlhdlrexprdata nlhdlr expression data
Definition at line 120 of file nlhdlr_perspective.c.
References NULL, SCIP_CALL, SCIP_OKAY, SCIPfreeBlockMemoryArray, SCIPfreeBlockMemoryArrayNull, and SCIPreleaseVar().
Referenced by SCIP_DECL_NLHDLRFREEEXPRDATA().
◆ removeIndicator()
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static |
- Parameters
-
scip SCIP data structure nlexprdata nlhdlr expression data pos position of the indicator
Definition at line 149 of file nlhdlr_perspective.c.
References SCIP_CALL, SCIP_OKAY, and SCIPreleaseVar().
Referenced by computeOffValues().
◆ addAuxVar()
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static |
adds an auxiliary variable to the vars array in nlhdlrexprdata
- Parameters
-
scip SCIP data structure nlhdlrexprdata nlhdlr expression data auxvarmap hashmap linking auxvars to positions in nlhdlrexprdata->vars auxvar variable to be added
Definition at line 172 of file nlhdlr_perspective.c.
References NULL, SCIP_CALL, SCIP_OKAY, SCIPcalcMemGrowSize(), SCIPcaptureVar(), SCIPhashmapGetImageInt(), SCIPhashmapSetImageInt(), and SCIPreallocBlockMemoryArray.
Referenced by computeOffValues().
◆ addSCVarIndicator()
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static |
adds an indicator to the data of a semicontinuous variable
- Parameters
-
scip SCIP data structure scvdata semicontinuous variable data indicator indicator to be added val0 value of the variable when indicator == 0 lb1 lower bound of the variable when indicator == 1 ub1 upper bound of the variable when indicator == 1
Definition at line 213 of file nlhdlr_perspective.c.
References SCVarData::bndssize, SCVarData::bvars, FALSE, SCVarData::lbs1, SCVarData::nbnds, NULL, SCIP_Bool, SCIP_CALL, SCIP_OKAY, SCIPcalcMemGrowSize(), SCIPreallocBlockMemoryArray, SCIPsortedvecFindPtr(), SCVarData::ubs1, and SCVarData::vals0.
Referenced by computeOffValues(), and varIsSemicontinuous().
◆ getSCVarDataInd()
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static |
find scvardata of var and position of indicator in it
If indicator is not there, returns NULL.
- Parameters
-
scvars hashmap linking variables to scvardata var variable indicator indicator variable pos pointer to store the position of indicator
Definition at line 282 of file nlhdlr_perspective.c.
References SCVarData::bvars, SCVarData::nbnds, NULL, SCIP_Bool, SCIPhashmapGetImage(), and SCIPsortedvecFindPtr().
Referenced by analyseVarOnoffBounds(), computeOffValues(), SCIP_DECL_NLHDLRENFO(), and tightenOnBounds().
◆ varIsSemicontinuous()
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static |
checks if a variable is semicontinuous and, if needed, updates the scvars hashmap
A variable \(x\) is semicontinuous if its bounds depend on at least one binary variable called the indicator, and indicator = 0 ⇒ \(x = x^0\) for some real constant \(x^0\).
- Parameters
-
scip SCIP data structure var the variable to check scvars semicontinuous variable information result buffer to store whether var is semicontinuous
Definition at line 316 of file nlhdlr_perspective.c.
References addSCVarIndicator(), SCVarData::bvars, FALSE, MAX, MIN, SCVarData::nbnds, NULL, SCIP_Bool, SCIP_CALL, SCIP_OKAY, SCIP_Real, SCIP_VARTYPE_BINARY, SCIPallocClearBlockMemory, SCIPdebugMsg, SCIPdebugMsgPrint, SCIPhashmapGetImage(), SCIPhashmapInsert(), SCIPisEQ(), SCIPsortedvecFindPtr(), SCIPvarGetLbGlobal(), SCIPvarGetName(), SCIPvarGetNVlbs(), SCIPvarGetNVubs(), SCIPvarGetType(), SCIPvarGetUbGlobal(), SCIPvarGetVlbCoefs(), SCIPvarGetVlbConstants(), SCIPvarGetVlbVars(), SCIPvarGetVubCoefs(), SCIPvarGetVubConstants(), SCIPvarGetVubVars(), TRUE, and SCVarData::vals0.
Referenced by exprIsSemicontinuous().
◆ exprIsSemicontinuous()
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static |
- Parameters
-
scip SCIP data structure nlhdlrdata nonlinear handler data nlhdlrexprdata nlhdlr expression data expr expression res buffer to store whether the expression is semicontinuous
Definition at line 479 of file nlhdlr_perspective.c.
References SCVarData::bvars, FALSE, SCVarData::nbnds, NULL, SCIP_Bool, SCIP_CALL, SCIP_EXPRITER_DFS, SCIP_OKAY, SCIPallocClearBufferArray, SCIPcaptureVar(), SCIPcomputeArraysIntersectionPtr(), SCIPcreateExpriter(), SCIPdebugMsg, SCIPduplicateBlockMemoryArray, SCIPexprGetChildren(), SCIPexprGetNChildren(), SCIPexpriterGetCurrent(), SCIPexpriterGetNext(), SCIPexpriterInit(), SCIPexpriterIsEnd(), SCIPfreeBlockMemoryArray, SCIPfreeBufferArrayNull, SCIPfreeExpriter(), SCIPgetVarExprVar(), SCIPhashmapGetImage(), SCIPisExprSum(), SCIPisExprVar(), SCIPreallocBlockMemoryArray, SCIPsortedvecFindPtr(), SCIPvarGetName(), SCIPvarIsRelaxationOnly(), TRUE, and varIsSemicontinuous().
Referenced by SCIP_DECL_NLHDLRDETECT().
◆ computeOffValues()
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static |
computes the 'off' value of the expression and the 'off' values of semicontinuous auxiliary variables for each indicator variable
- Parameters
-
scip SCIP data structure nlhdlrdata nonlinear handler data nlhdlrexprdata nlhdlr expression data expr expression
Definition at line 661 of file nlhdlr_perspective.c.
References addAuxVar(), addSCVarIndicator(), SCVarData::bndssize, SCVarData::bvars, FALSE, getSCVarDataInd(), SCVarData::lbs1, NULL, removeIndicator(), SCIP_Bool, SCIP_CALL, SCIP_EXPRITER_DFS, SCIP_INVALID, SCIP_OKAY, SCIP_Real, SCIPallocBlockMemoryArray, SCIPallocBufferArray, SCIPallocClearBlockMemory, SCIPblkmem(), SCIPcreateExpriter(), SCIPcreateSol(), SCIPdebugMsg, SCIPduplicateBufferArray, SCIPevalExpr(), SCIPexprGetEvalValue(), SCIPexpriterGetCurrent(), SCIPexpriterGetNext(), SCIPexpriterInit(), SCIPexpriterIsEnd(), SCIPfreeBufferArray, SCIPfreeExpriter(), SCIPfreeSol(), SCIPgetExprAuxVarNonlinear(), SCIPgetExprVarExprs(), SCIPgetVarExprVar(), SCIPhashmapCreate(), SCIPhashmapFree(), SCIPhashmapGetImage(), SCIPhashmapInsert(), SCIPisExprSum(), SCIPisExprVar(), SCIPreleaseExpr(), SCIPsetSolVals(), SCIPvarGetLbGlobal(), SCIPvarGetName(), SCIPvarGetUbGlobal(), TRUE, SCVarData::ubs1, and SCVarData::vals0.
Referenced by SCIP_DECL_NLHDLRINITSEPA().
◆ startProbing()
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static |
go into probing and set some variable bounds
- Parameters
-
scip SCIP data structure nlhdlrdata nonlinear handler data nlhdlrexprdata nlhdlr expression data indicator indicator variable probingvars array of vars whose bounds we will change in probing probingdoms array of intervals to which bounds of probingvars will be changed in probing nprobingvars number of probing vars sol solution to be separated solcopy buffer for a copy of sol before going into probing; if *solcopy == sol, then copy is created cutoff_probing pointer to store whether indicator == 1 is infeasible
Definition at line 839 of file nlhdlr_perspective.c.
References NULL, SCIP_Bool, SCIP_CALL, SCIP_Longint, SCIP_OKAY, SCIP_Real, SCIPchgVarLbProbing(), SCIPchgVarUbProbing(), SCIPcreateSol(), SCIPgetDepth(), SCIPgetSolVal(), SCIPintervalGetInf(), SCIPintervalGetSup(), SCIPisGT(), SCIPisLT(), SCIPnewProbingNode(), SCIPpropagateProbing(), SCIPsetSolVal(), SCIPstartProbing(), SCIPvarGetLbLocal(), and SCIPvarGetUbLocal().
Referenced by SCIP_DECL_NLHDLRENFO().
◆ analyseVarOnoffBounds()
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static |
analyse on/off bounds on a variable
analyses for
- tightening bounds in probing for indicator = 1,
- fixing indicator / detecting cutoff if one or both states are infeasible,
- tightening local bounds if indicator is fixed.
probinglb and probingub are only set if doprobing is TRUE. They are either set to bounds that should be used in probing or to SCIP_INVALID if bounds on var shouldn't be changed in probing.
- Parameters
-
scip SCIP data structure nlhdlrdata nonlinear handler data var variable indicator indicator variable indvalue indicator value for which the bounds are applied infeas pointer to store whether infeasibility has been detected probinglb pointer to store the lower bound to be applied in probing probingub pointer to store the upper bound to be applied in probing doprobing whether we currently consider to go into probing reduceddom pointer to store whether any variables were fixed
Definition at line 922 of file nlhdlr_perspective.c.
References FALSE, getSCVarDataInd(), SCVarData::lbs1, NULL, SCIP_Bool, SCIP_CALL, SCIP_INVALID, SCIP_OKAY, SCIP_Real, SCIPdebugMsg, SCIPfixVar(), SCIPisEQ(), SCIPisFeasGT(), SCIPisFeasLT(), SCIPisGT(), SCIPisLT(), SCIPtightenVarLb(), SCIPtightenVarUb(), SCIPvarGetLbLocal(), SCIPvarGetName(), SCIPvarGetUbLocal(), SCVarData::ubs1, and SCVarData::vals0.
Referenced by analyseOnoffBounds().
◆ analyseOnoffBounds()
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looks for bound tightenings to be applied either in the current node or in probing
Loops through both possible values of indicator and calls analyseVarOnoffBounds(). Might update the *doprobing flag by setting it to FALSE if:
- indicator is fixed or
- analyseVarOnoffBounds() hasn't found a sufficient improvement at indicator==1.
If *doprobing==TRUE, stores bounds suggested by analyseVarOnoffBounds() in order to apply them in probing together with the fixing indicator=1.
- Parameters
-
scip SCIP data structure nlhdlrdata nonlinear handler data nlhdlrexprdata nlhdlr expression data indicator indicator variable probingvars array to store variables whose bounds will be changed in probing probingdoms array to store bounds to be applied in probing nprobingvars pointer to store number of vars whose bounds will be changed in probing doprobing pointer to the flag telling whether we want to do probing result pointer to store the result
Definition at line 1080 of file nlhdlr_perspective.c.
References analyseVarOnoffBounds(), b, FALSE, NULL, SCIP_Bool, SCIP_CALL, SCIP_CUTOFF, SCIP_INVALID, SCIP_OKAY, SCIP_Real, SCIP_REDUCEDDOM, SCIPreallocBufferArray, SCIPvarGetLbLocal(), SCIPvarGetUbLocal(), and TRUE.
Referenced by SCIP_DECL_NLHDLRENFO().
◆ tightenOnBounds()
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saves local bounds on all expression variables, including auxiliary variables, obtained from propagating indicator == 1 to the corresponding SCVARDATA (should only be used in the root node)
- Parameters
-
nlhdlrexprdata nlhdlr expression data scvars hashmap with semicontinuous variables indicator indicator variable
Definition at line 1176 of file nlhdlr_perspective.c.
References getSCVarDataInd(), SCVarData::lbs1, MAX, MIN, NULL, SCIP_OKAY, SCIP_Real, SCIPvarGetLbLocal(), SCIPvarGetUbLocal(), and SCVarData::ubs1.
Referenced by SCIP_DECL_NLHDLRENFO().
◆ SCIP_DECL_NLHDLRCOPYHDLR()
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nonlinear handler copy callback
Definition at line 1212 of file nlhdlr_perspective.c.
References NLHDLR_NAME, NULL, SCIP_CALL, SCIP_OKAY, SCIPincludeNlhdlrPerspective(), and SCIPnlhdlrGetName().
◆ SCIP_DECL_NLHDLRFREEHDLRDATA()
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static |
callback to free data of handler
Definition at line 1226 of file nlhdlr_perspective.c.
References SCIP_OKAY, and SCIPfreeBlockMemory.
◆ SCIP_DECL_NLHDLRFREEEXPRDATA()
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static |
callback to free expression specific data
Definition at line 1236 of file nlhdlr_perspective.c.
References freeNlhdlrExprData(), SCIP_CALL, SCIP_OKAY, and SCIPfreeBlockMemory.
◆ SCIP_DECL_NLHDLREXIT()
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callback to be called in initialization callback to be called in deinitialization
Definition at line 1255 of file nlhdlr_perspective.c.
References SCVarData::bndssize, SCVarData::bvars, SCVarData::lbs1, NULL, SCIP_OKAY, SCIPfreeBlockMemory, SCIPfreeBlockMemoryArray, SCIPhashmapEntryGetImage(), SCIPhashmapFree(), SCIPhashmapGetEntry(), SCIPhashmapGetNEntries(), SCIPnlhdlrGetData(), SCVarData::ubs1, and SCVarData::vals0.
◆ SCIP_DECL_NLHDLRDETECT()
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callback to detect structure in expression tree
We are looking for expressions g(x), where x is a vector of semicontinuous variables that all share at least one indicator variable.
Definition at line 1293 of file nlhdlr_perspective.c.
References exprIsSemicontinuous(), FALSE, NULL, SCIP_Bool, SCIP_CALL, SCIP_NLHDLR_METHOD_SEPAABOVE, SCIP_NLHDLR_METHOD_SEPABELOW, SCIP_NLHDLR_METHOD_SEPABOTH, SCIP_OKAY, SCIPallocBlockMemoryArray, SCIPallocBufferArray, SCIPallocClearBlockMemory, SCIPblkmem(), SCIPcaptureVar(), SCIPdebugMsg, SCIPdebugMsgPrint, SCIPfreeBufferArray, SCIPgetExprEnfoDataNonlinear(), SCIPgetExprNAuxvarUsesNonlinear(), SCIPgetExprNEnfosNonlinear(), SCIPgetExprNVars(), SCIPgetExprVarExprs(), SCIPgetNBinVars(), SCIPgetNVars(), SCIPgetVarExprVar(), SCIPhashmapCreate(), SCIPinfoMessage(), SCIPisExprSum(), SCIPnlhdlrGetData(), SCIPnlhdlrGetName(), SCIPnlhdlrHasEstimate(), SCIPprintExpr(), SCIPreleaseExpr(), SCIPsortPtr(), and TRUE.
◆ SCIP_DECL_NLHDLREVALAUX()
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auxiliary evaluation callback of nonlinear handler
Definition at line 1428 of file nlhdlr_perspective.c.
References NULL, REALABS, SCIP_CALL, SCIP_INVALID, SCIP_NLHDLR_METHOD_SEPABOTH, SCIP_OKAY, SCIP_Real, SCIPgetExprAuxVarNonlinear(), SCIPgetExprEnfoDataNonlinear(), SCIPgetExprNEnfosNonlinear(), SCIPgetSolVal(), SCIPnlhdlrHasEstimate(), and SCIPsetExprEnfoAuxValueNonlinear().
◆ SCIP_DECL_NLHDLRINITSEPA()
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separation initialization method of a nonlinear handler
Definition at line 1474 of file nlhdlr_perspective.c.
References computeOffValues(), SCIP_CALL, SCIP_OKAY, SCIPfreeBlockMemoryArray, SCIPnlhdlrGetData(), and SCIPreallocBlockMemoryArray.
◆ SCIP_DECL_NLHDLRENFO()
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static |
nonlinear handler enforcement callback
"Perspectivies" cuts produced by other nonlinear handlers.
Suppose that we want to separate \(x\) from the set \(\{ x : g(x) \leq 0\}\). If \(g(x) = g^0\) if indicator \(z = 0\), and a cut is given by \(\sum_i a_ix_i + c \leq \text{aux}\), where \(x_i = x_i^0\) if \(z = 0\) for all \(i\), then the "perspectivied" cut is
\[\sum_i a_ix_i + c + (1 - z)\,(g^0 - c - \sum_i a_ix_i^0) \leq \text{aux}.\]
This ensures that at \(z = 1\), the new cut is equivalent to the given cut, and at \(z = 0\) it reduces to \(g^0 \leq \text{aux}\).
Definition at line 1521 of file nlhdlr_perspective.c.
References analyseOnoffBounds(), FALSE, getSCVarDataInd(), MAX, NULL, r, REALABS, SCIP_Bool, SCIP_BRANCHED, SCIP_CALL, SCIP_CUTOFF, SCIP_DIDNOTFIND, SCIP_DIDNOTRUN, SCIP_INVALIDRESULT, SCIP_NLHDLR_METHOD_SEPAABOVE, SCIP_NLHDLR_METHOD_SEPABELOW, SCIP_OKAY, SCIP_Real, SCIP_REDUCEDDOM, SCIP_SEPARATED, SCIP_VARSTATUS_FIXED, SCIPaddRowprepTerm(), SCIPallocBufferArray, SCIPclearPtrarray(), SCIPcreateBoolarray(), SCIPcreatePtrarray(), SCIPcreateSol(), SCIPdebugMsg, SCIPendProbing(), SCIPerrorMessage, SCIPfeastol(), SCIPfixVar(), SCIPfreeBoolarray(), SCIPfreeBufferArray, SCIPfreeBufferArrayNull, SCIPfreePtrarray(), SCIPfreeRowprep(), SCIPfreeSol(), SCIPgetBoolarrayVal(), SCIPgetDepth(), SCIPgetExprAbsAuxViolationNonlinear(), SCIPgetExprAuxVarNonlinear(), SCIPgetExprEnfoDataNonlinear(), SCIPgetExprNEnfosNonlinear(), SCIPgetPtrarrayMaxIdx(), SCIPgetPtrarrayMinIdx(), SCIPgetPtrarrayVal(), SCIPgetSolVal(), SCIPgetSubscipDepth(), SCIPinfoMessage(), SCIPinProbing(), SCIPisFeasEQ(), SCIPnlhdlrGetData(), SCIPnlhdlrGetName(), SCIPnlhdlrHasEstimate(), SCIPprintExpr(), SCIPprintRowprep(), SCIPprocessRowprepNonlinear(), SCIProwprepAddConstant(), SCIProwprepGetCoefs(), SCIProwprepGetName(), SCIProwprepGetNVars(), SCIProwprepGetSide(), SCIProwprepGetVars(), SCIPsetBoolarrayVal(), SCIPsetPtrarrayVal(), SCIPsetSolVal(), SCIPvarGetLbLocal(), SCIPvarGetName(), SCIPvarGetStatus(), SCIPvarGetUbLocal(), startProbing(), tightenOnBounds(), TRUE, and SCVarData::vals0.