1 /* * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * */ 2 /* */ 3 /* This file is part of the program and library */ 4 /* SCIP --- Solving Constraint Integer Programs */ 5 /* */ 6 /* Copyright (c) 2002-2023 Zuse Institute Berlin (ZIB) */ 7 /* */ 8 /* Licensed under the Apache License, Version 2.0 (the "License"); */ 9 /* you may not use this file except in compliance with the License. */ 10 /* You may obtain a copy of the License at */ 11 /* */ 12 /* http://www.apache.org/licenses/LICENSE-2.0 */ 13 /* */ 14 /* Unless required by applicable law or agreed to in writing, software */ 15 /* distributed under the License is distributed on an "AS IS" BASIS, */ 16 /* WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied. */ 17 /* See the License for the specific language governing permissions and */ 18 /* limitations under the License. */ 19 /* */ 20 /* You should have received a copy of the Apache-2.0 license */ 21 /* along with SCIP; see the file LICENSE. If not visit scipopt.org. */ 22 /* */ 23 /* * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * */ 24 25 /**@file sepa_gauge.h 26 * @ingroup SEPARATORS 27 * @brief gauge separator 28 * @author Felipe Serrano 29 * 30 * This separator receives a point \f$ x_0 \f$ to separate and, given an interior point \f$ \bar x \f$, finds the 31 * intersection between the boundary of a convex relaxation of the current problem and the segment joining \f$ x_0 \f$ 32 * and \f$ \bar x \f$. Then it generates gradient cuts at the intersection. 33 * 34 * The interior point \f$ \bar x \f$ is computed only once, by solving 35 * \f{align}{ 36 * \min \; & t \\ 37 * s.t. \; & g_j(x) \le t & \forall j=1,\ldots,m \\ 38 * & l_k(x) \le 0 & \forall k=1,\ldots,p 39 * \f} 40 * where each \f$ g_j \f$ is a convex function and \f$ l_k \f$ is a linear function and 41 * \f[ 42 * C = \{ x \colon g_j(x) \le 0 \, \forall j=1,\ldots,m, l_k(x) \le 0 \, \forall k=1,\ldots,p \} 43 * \f] 44 * is a convex relaxation of the current problem. 45 * If we can not find an interior solution, the separator will not be executed again. 46 * 47 * Note that we do not try to push the linear constraints into the interior, i.e. we use \f$ l_k(x) \le 0 \f$ instead 48 * of \f$ l_k(x) \le t \f$, since some of the inequalities might actually be equalities, forcing \f$ t \f$ to zero. 49 * We also use an arbitrary lower bound on \f$ t \f$ to handle the case when \f$ C \f$ is unbounded. 50 * 51 * By default, the separator, if enabled, runs only if the convex relaxation has at least two nonlinear convex constraints. 52 * 53 * In order to compute the boundary point, we consider only nonlinear convex constraints that are violated by the point 54 * we want to separate. These constraints define a convex region for which \f$ \bar x \f$ is an interior point. Then, 55 * a binary search is perform on the segment \f$[\bar x, x_0]\f$ in order to find the boundary point. Gradient cuts are 56 * computed for each of these nonlinear convex constraints which are active at the boundary point. 57 * 58 * Technical details: 59 * - We consider a constraint for the binary search only when its violation is larger than \f$ 10^{-4} \f$, see 60 * MIN_VIOLATION in sepa_gauge.c. The reason is that if the violation is too small, chances are that the point in the 61 * boundary is in the interior for this constraint and we wouldn't generate a cut for it anyway. On the other hand, 62 * even if we generate a cut for this constraint, it is likely that the boundary point is very close to the point to 63 * separate. Hence the cut generated would be very similar to the gradient cut at the point to separate. 64 * - Before separating, if a slight perturbation of the interior point in the direction of the point to separate 65 * gives a point outside the region, we do not separate. The reason is that the interior point we computed could be 66 * almost at the boundary and the segment \f$[\bar x, x_0]\f$ could be tangent to the region. In that case, the cuts 67 * we generate will not separate \f$ x_0 \f$ from the feasible region. 68 * 69 * This separator is currently disabled by default. It requires additional 70 * tuning to be enabled by default. However, it may be useful to enable 71 * it on instances with convex nonlinear constraints if SCIP spends 72 * many iterations in the separation loop without doing sufficient progress. 73 */ 74 75 /*---+----1----+----2----+----3----+----4----+----5----+----6----+----7----+----8----+----9----+----0----+----1----+----2*/ 76 77 #ifndef __SCIP_SEPA_GAUGE_H__ 78 #define __SCIP_SEPA_GAUGE_H__ 79 80 81 #include "scip/def.h" 82 #include "scip/type_retcode.h" 83 #include "scip/type_scip.h" 84 85 #ifdef __cplusplus 86 extern "C" { 87 #endif 88 89 /** creates the gauge separator and includes it in SCIP 90 * 91 * @ingroup SeparatorIncludes 92 */ 93 SCIP_EXPORT 94 SCIP_RETCODE SCIPincludeSepaGauge( 95 SCIP* scip /**< SCIP data structure */ 96 ); 97 98 #ifdef __cplusplus 99 } 100 #endif 101 102 #endif 103