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4    	/*         SCIP --- Solving Constraint Integer Programs                      */
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24   	
25   	/**@file   benderscut_opt.h
26   	 * @ingroup BENDERSCUTS
27   	 * @brief  Generates a standard Benders' decomposition optimality cut
28   	 * @author Stephen J. Maher
29   	 *
30   	 * The classical Benders' decomposition optimality cuts arise from a feasible instance of the Benders' decomposition
31   	 * subproblem. The optimality cuts are an underestimator of the subproblem objective function value. Auxiliary
32   	 * variables, \f$\varphi\f$ are added to the master problem as a lower bound on the subproblem objective function value.
33   	 *
34   	 * Consider a linear Benders' decomposition subproblem that takes the master problem solution \f$\bar{x}\f$ as input:
35   	 * \f[
36   	 * z(\bar{x}) = \min\{d^{T}y : Ty \geq h - H\bar{x}, y \geq 0\}
37   	 * \f]
38   	 * If the subproblem is feasible, and \f$z(\bar{x}) > \varphi\f$ (indicating that the current underestimators are not
39   	 * optimal) then the Benders' decomposition optimality cut can be generated from the optimal dual solution of the
40   	 * subproblem. Let \f$w\f$ be the vector corresponding to the optimal dual solution of the Benders' decomposition
41   	 * subproblem. The resulting cut is:
42   	 * \f[
43   	 * \varphi \geq w^{T}(h - Hx)
44   	 * \f]
45   	 *
46   	 * Next, consider a nonlinear Benders' decomposition subproblem that takes the master problem solution \f$\bar{x}\f$ as input:
47   	 * \f[
48   	 * z(\bar{x}) = \min\{d^{T}y : g(\bar{x},y) \leq 0, y \geq 0\}
49   	 * \f]
50   	 * If the subproblem is feasible, and \f$z(\bar{x}) > \varphi\f$ (indicating that the current underestimators are not
51   	 * optimal) then the Benders' decomposition optimality cut can be generated from the optimal dual solution of the
52   	 * subproblem. Let \f$w\f$ be the vector corresponding to the optimal dual solution of the Benders' decomposition subproblem.
53   	 * The resulting cut is:
54   	 * \f[
55   	 * \varphi \geq z(\bar{x}) + w^{T} \nabla_x g(\bar{x}, y) (x-\bar{x})
56   	 * \f]
57   	 *
58   	 */
59   	
60   	/*---+----1----+----2----+----3----+----4----+----5----+----6----+----7----+----8----+----9----+----0----+----1----+----2*/
61   	
62   	#ifndef __SCIP_BENDERSCUT_OPT_H__
63   	#define __SCIP_BENDERSCUT_OPT_H__
64   	
65   	
66   	#include "scip/def.h"
67   	#include "scip/type_benders.h"
68   	#include "scip/type_benderscut.h"
69   	#include "scip/type_cons.h"
70   	#include "scip/type_lp.h"
71   	#include "scip/type_misc.h"
72   	#include "scip/type_nlp.h"
73   	#include "scip/type_retcode.h"
74   	#include "scip/type_scip.h"
75   	#include "scip/type_exprinterpret.h"
76   	
77   	#ifdef __cplusplus
78   	extern "C" {
79   	#endif
80   	
81   	/** creates the optimality Benders' decomposition cut and includes it in SCIP
82   	 *
83   	 *  @ingroup BenderscutIncludes
84   	 */
85   	SCIP_EXPORT
86   	SCIP_RETCODE SCIPincludeBenderscutOpt(
87   	   SCIP*                 scip,               /**< SCIP data structure */
88   	   SCIP_BENDERS*         benders             /**< Benders' decomposition */
89   	   );
90   	
91   	/** @addtogroup BENDERSCUTS
92   	 * @{
93   	 */
94   	
95   	/** Generates a classical Benders' optimality cut using the dual solutions from the subproblem or the input arrays. If
96   	 *  the dual solutions are input as arrays, then a mapping between the array indices and the rows/variables is required.
97   	 *  This method can also be used to generate a feasiblity, is a problem to minimise the infeasibilities has been solved
98   	 *  to generate the dual solutions
99   	 */
100  	SCIP_EXPORT
101  	SCIP_RETCODE SCIPgenerateAndApplyBendersOptCut(
102  	   SCIP*                 masterprob,         /**< the SCIP instance of the master problem */
103  	   SCIP*                 subproblem,         /**< the SCIP instance of the pricing problem */
104  	   SCIP_BENDERS*         benders,            /**< the benders' decomposition */
105  	   SCIP_BENDERSCUT*      benderscut,         /**< the benders' decomposition cut method */
106  	   SCIP_SOL*             sol,                /**< primal CIP solution */
107  	   int                   probnumber,         /**< the number of the pricing problem */
108  	   char*                 cutname,            /**< the name for the cut to be generated */
109  	   SCIP_Real             objective,          /**< the objective function of the subproblem */
110  	   SCIP_Real*            primalvals,         /**< the primal solutions for the NLP, can be NULL */
111  	   SCIP_Real*            consdualvals,       /**< dual variables for the constraints, can be NULL */
112  	   SCIP_Real*            varlbdualvals,      /**< the dual variables for the variable lower bounds, can be NULL */
113  	   SCIP_Real*            varubdualvals,      /**< the dual variables for the variable upper bounds, can be NULL */
114  	   SCIP_HASHMAP*         row2idx,            /**< mapping between the row in the subproblem to the index in the dual array, can be NULL */
115  	   SCIP_HASHMAP*         var2idx,            /**< mapping from variable of the subproblem to the index in the dual arrays, can be NULL */
116  	   SCIP_BENDERSENFOTYPE  type,               /**< the enforcement type calling this function */
117  	   SCIP_Bool             addcut,             /**< should the Benders' cut be added as a cut or constraint */
118  	   SCIP_Bool             feasibilitycut,     /**< is this called for the generation of a feasibility cut */
119  	   SCIP_RESULT*          result              /**< the result from solving the subproblems */
120  	   );
121  	
122  	/** adds the gradient of a nonlinear row in the current NLP solution of a subproblem to a linear row or constraint in the master problem
123  	 *
124  	 * Only computes gradient w.r.t. master problem variables.
125  	 * Computes also the directional derivative, that is, mult times gradient times solution.
126  	 */
127  	SCIP_EXPORT
128  	SCIP_RETCODE SCIPaddNlRowGradientBenderscutOpt(
129  	   SCIP*                 masterprob,         /**< the SCIP instance of the master problem */
130  	   SCIP*                 subproblem,         /**< the SCIP instance of the subproblem */
131  	   SCIP_BENDERS*         benders,            /**< the benders' decomposition structure */
132  	   SCIP_NLROW*           nlrow,              /**< nonlinear row */
133  	   SCIP_Real             mult,               /**< multiplier */
134  	   SCIP_Real*            primalvals,         /**< the primal solutions for the NLP, can be NULL */
135  	   SCIP_HASHMAP*         var2idx,            /**< mapping from variable of the subproblem to the index in the dual arrays, can be NULL */
136  	   SCIP_Real*            dirderiv,           /**< storage to add directional derivative */
137  	   SCIP_VAR***           vars,               /**< pointer to array of variables in the generated cut with non-zero coefficient */
138  	   SCIP_Real**           vals,               /**< pointer to array of coefficients of the variables in the generated cut */
139  	   int*                  nvars,              /**< the number of variables in the cut */
140  	   int*                  varssize            /**< the number of variables in the array */
141  	   );
142  	
143  	/** @} */
144  	
145  	#ifdef __cplusplus
146  	}
147  	#endif
148  	
149  	#endif
150