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2    	/*                                                                           */
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4    	/*         SCIP --- Solving Constraint Integer Programs                      */
5    	/*                                                                           */
6    	/*  Copyright (c) 2002-2023 Zuse Institute Berlin (ZIB)                      */
7    	/*                                                                           */
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19   	/*                                                                           */
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22   	/*                                                                           */
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24   	
25   	/**@file   presol_dualinfer.h
26   	 * @ingroup PRESOLVERS
27   	 * @brief  dual inference presolver
28   	 * @author Dieter Weninger
29   	 * @author Patrick Gemander
30   	 *
31   	 * This presolver does bound strengthening on continuous variables (columns) for getting bounds on dual variables y.
32   	 * The bounds of the dual variables are then used to fix primal variables or change the side of constraints.
33   	 * For ranged rows one needs to decide which side (rhs or lhs) determines the equality.
34   	 *
35   	 * We distinguish two cases concerning complementary slackness:
36   	 * i)  reduced cost fixing:       c_j - sup_y(y^T A_{.j}) > 0 => x_j = l_j
37   	 *                                c_j - inf_y(y^T A_{.j}) < 0 => x_j = u_j
38   	 * ii) positive dual lower bound: y_i > 0 =>  A_{i.}x = b_i
39   	 *
40   	 * Further information on this presolving approach are given in
41   	 * Achterberg et al. "Presolve reductions in mixed integer programming"
42   	 * and for a two-column extension in
43   	 * Chen et al. "Two-row and two-column mixed-integer presolve using hasing-based pairing methods".
44   	 */
45   	
46   	/*---+----1----+----2----+----3----+----4----+----5----+----6----+----7----+----8----+----9----+----0----+----1----+----2*/
47   	
48   	#ifndef __SCIP_PRESOL_DUALINFER_H__
49   	#define __SCIP_PRESOL_DUALINFER_H__
50   	
51   	#include "scip/def.h"
52   	#include "scip/type_retcode.h"
53   	#include "scip/type_scip.h"
54   	
55   	#ifdef __cplusplus
56   	extern "C" {
57   	#endif
58   	
59   	/** creates the dual inference presolver and includes it in SCIP
60   	 *
61   	 * @ingroup PresolverIncludes
62   	 */
63   	SCIP_EXPORT
64   	SCIP_RETCODE SCIPincludePresolDualinfer(
65   	   SCIP*                 scip                /**< SCIP data structure */
66   	   );
67   	
68   	#ifdef __cplusplus
69   	}
70   	#endif
71   	
72   	#endif
73