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sepa_minor.h
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/* * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * */
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/* */
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/* This file is part of the program and library */
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/* SCIP --- Solving Constraint Integer Programs */
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/* */
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/* Copyright (c) 2002-2024 Zuse Institute Berlin (ZIB) */
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/* */
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/* Licensed under the Apache License, Version 2.0 (the "License"); */
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/* you may not use this file except in compliance with the License. */
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/* You may obtain a copy of the License at */
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/* */
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/* http://www.apache.org/licenses/LICENSE-2.0 */
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/* */
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/* Unless required by applicable law or agreed to in writing, software */
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/* distributed under the License is distributed on an "AS IS" BASIS, */
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/* WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied. */
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/* See the License for the specific language governing permissions and */
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/* limitations under the License. */
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/* */
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/* You should have received a copy of the Apache-2.0 license */
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/* along with SCIP; see the file LICENSE. If not visit scipopt.org. */
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/* */
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/* * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * */
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/**@file sepa_minor.h
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* @ingroup SEPARATORS
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* @brief principal minor separator
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* @author Benjamin Mueller
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*
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* This separator detects all principal minors of the matrix \f$ xx' \f$ for which all auxiliary variables \f$ X \f$
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* exist, i.e., two indices \f$ i \neq j \f$ such that \f$ X_{ii} \f$, \f$ X_{jj} \f$, and \f$ X_{ij} \f$ exist. Because
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* \f$ X - xx' \f$ is required to be positive semi-definite, it follows that the matrix
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*
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* \f[
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* A(x,X) = \begin{bmatrix} 1 & x_i & x_j \\ x_i & X_{ii} & X_{ij} \\ x_j & X_{ij} & X_{jj} \end{bmatrix}
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* \f]
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*
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* is also required to be positive semi-definite. Let \f$ v \f$ be a negative eigenvector for \f$ A(x^*,X^*) \f$ in a
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* point \f$ (x^*,X^*) \f$, which implies that \f$ v' A(x^*,X^*) v < 0 \f$. To cut off \f$ (x^*,X^*) \f$, the separator
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* computes the globally valid linear inequality \f$ v' A(x,X) v \ge 0 \f$.
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*
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*
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* To identify which entries of the matrix X exist, we (the separator) iterate over the available nonlinear constraints.
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* For each constraint, we explore its expression and collect all nodes (expressions) of the form
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* - \f$x^2\f$
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* - \f$y \cdot z\f$
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*
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* Then, we go through the found bilinear terms \f$(yz)\f$ and if the corresponding \f$y^2\f$ and \f$z^2\f$ exist, then we have found
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* a minor.
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*
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* For circle packing instances, the minor cuts are not really helpful (see [Packing circles in a square: a theoretical
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* comparison of various convexification techniques](http://www.optimization-online.org/DB_HTML/2017/03/5911.html)).
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* Furthermore, the performance was negatively affected, thus circle packing constraint are identified and ignored in
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* the above algorithm. This behavior is controlled with the parameter "separating/minor/ignorepackingconss".
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*/
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/*---+----1----+----2----+----3----+----4----+----5----+----6----+----7----+----8----+----9----+----0----+----1----+----2*/
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#ifndef __SCIP_SEPA_MINOR_H__
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#define __SCIP_SEPA_MINOR_H__
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#include "
scip/scip.h
"
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#ifdef __cplusplus
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extern
"C"
{
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#endif
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/** creates the minor separator and includes it in SCIP
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*
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* @ingroup SeparatorIncludes
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*/
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SCIP_EXPORT
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SCIP_RETCODE
SCIPincludeSepaMinor
(
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SCIP
*
scip
/**< SCIP data structure */
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);
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/**@addtogroup SEPARATORS
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*
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* @{
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*/
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/** @} */
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#ifdef __cplusplus
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}
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#endif
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#endif
SCIPincludeSepaMinor
SCIP_RETCODE SCIPincludeSepaMinor(SCIP *scip)
Definition
sepa_minor.c:880
scip
Definition
objbenders.h:44
scip.h
SCIP callable library.
Scip
Definition
struct_scip.h:70
SCIP_RETCODE
enum SCIP_Retcode SCIP_RETCODE
Definition
type_retcode.h:63
sepa_minor.h
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