# SCIP

Solving Constraint Integer Programs

benderscut_feasalt.h
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2 /* */
3 /* This file is part of the program and library */
4 /* SCIP --- Solving Constraint Integer Programs */
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24
25 /**@file benderscut_feasalt.h
26  * @ingroup BENDERSCUTS
27  * @brief Alternative feasibility cuts for Benders' decomposition
28  * @author Stephen J. Maher
29  *
30  * The alternative feasibility cut for Benders' decomposition uses the optimality cut generation code to generate a cut
31  * that minimises the violation of the constraints.
32  * Consider the linear Benders' decomposition subproblem that takes the master problem solution \f$\bar{x}\f$ as input:
33  * \f[
34  * z(\bar{x}) = \min\{d^{T}y : Ty \geq h - H\bar{x}, y \geq 0\}
35  * \f]
36  * If the subproblem is infeasible as a result of the solution \f$\bar{x}\f$, then some of the constraints are violated.
37  * In this case, we define an alternative/auxiliary subproblem to find a solution that minimises the constraint
38  * violations. Such a problem is given by
39  * \f[
40  * \min\{\mathbb{1}{T}v : Ty + v \geq h - H\bar{x}, y \geq 0, v \geq 0\}
41  * \f]
42  *
43  * This auxiliary problem is guaranteed to always be feasible. Given a solution to this problem, it is possible to
44  * generate a classical Benders' optimality cut. For such a cut, the reader is referred to \ref benderscut_opt.h.
45  *
46  * If the Benders' decomposition subproblem contains non-linear constraints, an equivalent auxiliary subproblem can be
47  * formed to generate an alternative feasibility cut.
48  */
49
50 /*---+----1----+----2----+----3----+----4----+----5----+----6----+----7----+----8----+----9----+----0----+----1----+----2*/
51
52 #ifndef __SCIP_BENDERSCUT_FEASALT_H__
53 #define __SCIP_BENDERSCUT_FEASALT_H__
54
55
56 #include "scip/def.h"
57 #include "scip/type_benders.h"
58 #include "scip/type_retcode.h"
59 #include "scip/type_scip.h"
60
61 #ifdef __cplusplus
62 extern "C" {
63 #endif
64
65 /** creates the Alternative Feasibility Benders' decomposition cuts and includes it in SCIP
66  *
67  * @ingroup BenderscutIncludes
68  */
69 SCIP_EXPORT
71  SCIP* scip, /**< SCIP data structure */
72  SCIP_BENDERS* benders /**< Benders' decomposition */
73  );
74
75 #ifdef __cplusplus
76 }
77 #endif
78
79 #endif
enum SCIP_Retcode SCIP_RETCODE
Definition: type_retcode.h:63
type definitions for return codes for SCIP methods
type definitions for SCIP&#39;s main datastructure
SCIP_RETCODE SCIPincludeBenderscutFeasalt(SCIP *scip, SCIP_BENDERS *benders)
type definitions for Benders&#39; decomposition methods
common defines and data types used in all packages of SCIP