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24   	
25   	/**@file   nlhdlr_bilinear.h
26   	 * @ingroup NLHDLRS
27   	 * @brief  bilinear nonlinear handler
28   	 * @author Benjamin Mueller
29   	 */
30   	
31   	/*---+----1----+----2----+----3----+----4----+----5----+----6----+----7----+----8----+----9----+----0----+----1----+----2*/
32   	
33   	#ifndef __SCIP_NLHDLR_BILINEAR_H__
34   	#define __SCIP_NLHDLR_BILINEAR_H__
35   	
36   	#include "scip/scip.h"
37   	#include "scip/pub_nlhdlr.h"
38   	
39   	#ifdef __cplusplus
40   	extern "C" {
41   	#endif
42   	
43   	/** includes bilinear nonlinear handler in nonlinear constraint handler
44   	 *
45   	 * @ingroup NlhdlrIncludes
46   	 */
47   	SCIP_EXPORT
48   	SCIP_RETCODE SCIPincludeNlhdlrBilinear(
49   	   SCIP*                 scip                /**< SCIP data structure */
50   	   );
51   	
52   	/**@addtogroup NLHDLRS
53   	 * @{
54   	 *
55   	 * @name Bilinear nonlinear handler
56   	 *
57   	 * This nonlinear handler detects and collects bilinear terms and provides specialized propagation and estimation functionality.
58   	 *
59   	 * @{
60   	 */
61   	
62   	/** returns an array of expressions that have been detected by the bilinear nonlinear handler */
63   	SCIP_EXPORT
64   	SCIP_EXPR** SCIPgetExprsBilinear(
65   	   SCIP_NLHDLR*          nlhdlr              /**< nonlinear handler */
66   	   );
67   	
68   	/** returns an array of nonlinear handler expressions data of expressions that have been detected by the bilinear nonlinear handler */
69   	SCIP_EXPORT
70   	SCIP_NLHDLREXPRDATA** SCIPgetExprsdataBilinear(
71   	   SCIP_NLHDLR*          nlhdlr              /**< nonlinear handler */
72   	   );
73   	
74   	/** returns the total number of expressions that have been detected by the bilinear nonlinear handler */
75   	SCIP_EXPORT
76   	int SCIPgetNExprsBilinear(
77   	   SCIP_NLHDLR*          nlhdlr              /**< nonlinear handler */
78   	   );
79   	
80   	/** adds a globally valid inequality of the form \f$\text{xcoef}\cdot x \leq \text{ycoef} \cdot y + \text{constant}\f$ to a product expression of the form \f$x\cdot y\f$ */
81   	SCIP_EXPORT
82   	SCIP_RETCODE SCIPaddIneqBilinear(
83   	   SCIP*                 scip,               /**< SCIP data structure */
84   	   SCIP_NLHDLR*          nlhdlr,             /**< nonlinear handler */
85   	   SCIP_EXPR*            expr,               /**< product expression */
86   	   SCIP_Real             xcoef,              /**< x coefficient */
87   	   SCIP_Real             ycoef,              /**< y coefficient */
88   	   SCIP_Real             constant,           /**< constant part */
89   	   SCIP_Bool*            success             /**< buffer to store whether inequality has been accepted */
90   	   );
91   	
92   	/** computes coefficients of linearization of a bilinear term in a reference point */
93   	SCIP_EXPORT
94   	void SCIPaddBilinLinearization(
95   	   SCIP*                 scip,               /**< SCIP data structure */
96   	   SCIP_Real             bilincoef,          /**< coefficient of bilinear term */
97   	   SCIP_Real             refpointx,          /**< point where to linearize first  variable */
98   	   SCIP_Real             refpointy,          /**< point where to linearize second variable */
99   	   SCIP_Real*            lincoefx,           /**< buffer to add coefficient of first  variable in linearization */
100  	   SCIP_Real*            lincoefy,           /**< buffer to add coefficient of second variable in linearization */
101  	   SCIP_Real*            linconstant,        /**< buffer to add constant of linearization */
102  	   SCIP_Bool*            success             /**< buffer to set to FALSE if linearization has failed due to large numbers */
103  	   );
104  	
105  	/** computes coefficients of McCormick under- or overestimation of a bilinear term */
106  	SCIP_EXPORT
107  	void SCIPaddBilinMcCormick(
108  	   SCIP*                 scip,               /**< SCIP data structure */
109  	   SCIP_Real             bilincoef,          /**< coefficient of bilinear term */
110  	   SCIP_Real             lbx,                /**< lower bound on first variable */
111  	   SCIP_Real             ubx,                /**< upper bound on first variable */
112  	   SCIP_Real             refpointx,          /**< reference point for first variable */
113  	   SCIP_Real             lby,                /**< lower bound on second variable */
114  	   SCIP_Real             uby,                /**< upper bound on second variable */
115  	   SCIP_Real             refpointy,          /**< reference point for second variable */
116  	   SCIP_Bool             overestimate,       /**< whether to compute an overestimator instead of an underestimator */
117  	   SCIP_Real*            lincoefx,           /**< buffer to add coefficient of first  variable in linearization */
118  	   SCIP_Real*            lincoefy,           /**< buffer to add coefficient of second variable in linearization */
119  	   SCIP_Real*            linconstant,        /**< buffer to add constant of linearization */
120  	   SCIP_Bool*            success             /**< buffer to set to FALSE if linearization has failed due to large numbers */
121  	   );
122  	
123  	/** computes coefficients of linearization of a bilinear term in a reference point when given a linear inequality
124  	 *  involving only the variables of the bilinear term
125  	 *
126  	 *  @note the formulas are extracted from "Convex envelopes of bivariate functions through the solution of KKT systems"
127  	 *        by Marco Locatelli
128  	 */
129  	SCIP_EXPORT
130  	void SCIPcomputeBilinEnvelope1(
131  	   SCIP*                 scip,               /**< SCIP data structure */
132  	   SCIP_Real             bilincoef,          /**< coefficient of bilinear term */
133  	   SCIP_Real             lbx,                /**< lower bound on first variable */
134  	   SCIP_Real             ubx,                /**< upper bound on first variable */
135  	   SCIP_Real             refpointx,          /**< reference point for first variable */
136  	   SCIP_Real             lby,                /**< lower bound on second variable */
137  	   SCIP_Real             uby,                /**< upper bound on second variable */
138  	   SCIP_Real             refpointy,          /**< reference point for second variable */
139  	   SCIP_Bool             overestimate,       /**< whether to compute an overestimator instead of an underestimator */
140  	   SCIP_Real             xcoef,              /**< x coefficient of linear inequality; must be in {-1,0,1} */
141  	   SCIP_Real             ycoef,              /**< y coefficient of linear inequality */
142  	   SCIP_Real             constant,           /**< constant of linear inequality */
143  	   SCIP_Real* RESTRICT   lincoefx,           /**< buffer to store coefficient of first  variable in linearization */
144  	   SCIP_Real* RESTRICT   lincoefy,           /**< buffer to store coefficient of second variable in linearization */
145  	   SCIP_Real* RESTRICT   linconstant,        /**< buffer to store constant of linearization */
146  	   SCIP_Bool* RESTRICT   success             /**< buffer to store whether linearization was successful */
147  	   );
148  	
149  	/** computes coefficients of linearization of a bilinear term in a reference point when given two linear inequalities
150  	 *  involving only the variables of the bilinear term
151  	 *
152  	 *  @note the formulas are extracted from "Convex envelopes of bivariate functions through the solution of KKT systems"
153  	 *        by Marco Locatelli
154  	 */
155  	SCIP_EXPORT
156  	void SCIPcomputeBilinEnvelope2(
157  	   SCIP*                 scip,               /**< SCIP data structure */
158  	   SCIP_Real             bilincoef,          /**< coefficient of bilinear term */
159  	   SCIP_Real             lbx,                /**< lower bound on first variable */
160  	   SCIP_Real             ubx,                /**< upper bound on first variable */
161  	   SCIP_Real             refpointx,          /**< reference point for first variable */
162  	   SCIP_Real             lby,                /**< lower bound on second variable */
163  	   SCIP_Real             uby,                /**< upper bound on second variable */
164  	   SCIP_Real             refpointy,          /**< reference point for second variable */
165  	   SCIP_Bool             overestimate,       /**< whether to compute an overestimator instead of an underestimator */
166  	   SCIP_Real             alpha1,             /**< x coefficient of linear inequality; must be in {-1,0,1} */
167  	   SCIP_Real             beta1,              /**< y coefficient of linear inequality */
168  	   SCIP_Real             gamma1,             /**< constant of linear inequality */
169  	   SCIP_Real             alpha2,             /**< x coefficient of linear inequality; must be in {-1,0,1} */
170  	   SCIP_Real             beta2,              /**< y coefficient of linear inequality */
171  	   SCIP_Real             gamma2,             /**< constant of linear inequality */
172  	   SCIP_Real* RESTRICT   lincoefx,           /**< buffer to store coefficient of first  variable in linearization */
173  	   SCIP_Real* RESTRICT   lincoefy,           /**< buffer to store coefficient of second variable in linearization */
174  	   SCIP_Real* RESTRICT   linconstant,        /**< buffer to store constant of linearization */
175  	   SCIP_Bool* RESTRICT   success             /**< buffer to store whether linearization was successful */
176  	   );
177  	
178  	/** @}
179  	  * @}
180  	  */
181  	
182  	#ifdef __cplusplus
183  	}
184  	#endif
185  	
186  	#endif /* __SCIP_NLHDLR_BILINEAR_H__ */
187