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2    	/*                                                                           */
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4    	/*         SCIP --- Solving Constraint Integer Programs                      */
5    	/*                                                                           */
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7    	/*                                                                           */
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22   	/*                                                                           */
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24   	
25   	/**@file   presol_tworowbnd.h
26   	 * @ingroup DEFPLUGINS_PRESOL
27   	 * @brief  do bound tightening by using two rows
28   	 * @author Dieter Weninger
29   	 * @author Patrick Gemander
30   	 *
31   	 * Perform bound tightening on two inequalities with some common variables.
32   	 * Two possible methods are being used.
33   	 *
34   	 * 1. LP-bound
35   	 * Let two constraints be given:
36   	 * \f{eqnarray*}{
37   	 *   A_{iR} x_R + A_{iS} x_S              \geq b_i\\
38   	 *   A_{kR} x_R              + A_{kT} x_T \geq b_k
39   	 * \f}
40   	 * with \f$N\f$ the set of variable indexes, \f$R \subseteq N\f$, \f$S \subseteq N\f$, \f$T \subseteq N\f$,
41   	 * \f$R \cap S = \emptyset\f$, \f$R \cap T = \emptyset\f$, \f$S \cap T = \emptyset\f$ and row indices \f$i \not= k\f$.
42   	 *
43   	 * Let \f$\ell\f$ and \f$u\f$ be bound vectors for x and solve the following two LPs
44   	 * \f{eqnarray*}{
45   	 *   L = \min \{ A_{kR} x_R : A_{iR} x_R + A_{iS} x_S \geq b_i, \ell \leq x \leq u \}\\
46   	 *   U = \max \{ A_{kR} x_R : A_{iR} x_R + A_{iS} x_S \geq b_i, \ell \leq x \leq u \}
47   	 * \f}
48   	 * and use \f$L\f$ and \f$U\f$ for getting bounds on \f$x_T\f$.
49   	 *
50   	 * If \f$L + \mbox{infimum}(A_{kT}x_T) \geq b_k\f$, then the second constraint above is redundant.
51   	 *
52   	 * 2. ConvComb with clique-extension
53   	 * Given two constraints
54   	 * \f{eqnarray*}{
55   	 *     A_{i\cdot} x \geq b_i \\
56   	 *     A_{k\cdot} x \geq b_k \\
57   	 *     \ell \leq x \leq u \\
58   	 * \f}
59   	 * this method determines promising values for \f$\lambda \in (0,1)\f$ and
60   	 * applies feasibility-based bound tightening to the convex combinations
61   	 *
62   	 * \f$(\lambda A_{i\cdot} + (1 - \lambda) A_{k\cdot}) x \geq \lambda b_i + (1 - \lambda) b_k\f$.
63   	 *
64   	 * Additionally, cliques drawn from the SCIPcliqueTable are used
65   	 * to further strengthen the above bound tightening. Full details can be found in
66   	 *    - Belotti P. "Bound reduction using pairs of linear inequalities"
67   	 *    - Chen W. et. al "Two-row and two-column mixed-integer presolve using hashing-based pairing methods"
68   	 */
69   	
70   	/*---+----1----+----2----+----3----+----4----+----5----+----6----+----7----+----8----+----9----+----0----+----1----+----2*/
71   	
72   	#ifndef __SCIP_PRESOL_TWOROWBND_H__
73   	#define __SCIP_PRESOL_TWOROWBND_H__
74   	
75   	#include "scip/def.h"
76   	#include "scip/type_retcode.h"
77   	#include "scip/type_scip.h"
78   	
79   	#ifdef __cplusplus
80   	extern "C" {
81   	#endif
82   	
83   	/** creates the tworowbnd presolver and includes it in SCIP
84   	 *
85   	 * @ingroup PresolverIncludes
86   	 */
87   	SCIP_EXPORT
88   	SCIP_RETCODE SCIPincludePresolTworowbnd(
89   	   SCIP*                 scip                /**< SCIP data structure */
90   	   );
91   	
92   	#ifdef __cplusplus
93   	}
94   	#endif
95   	
96   	#endif
97