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Laboratoire d'informatique fondamentale de Marseille UMR 6166 - CNRS, Université de la Méditerranée, Université de Provence |
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Laboratoire d'informatique fondamentale de Marseille UMR 6166 - CNRS, Université de la Méditerranée, Université de Provence |
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| HAL: hal-00421760, version 1 |
| DOI: 10.1007/978-3-540-68891-4_2 |
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| 13th International Conference, IPCO 2008, Bertinoro, Italy : France (2008) |
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| Disjunctive Cuts for Non-convex Mixed Integer Quadratically Constrained Programs |
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| Anureet Saxena 1Pierre Bonami 2 |
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| (2008-05-24) |
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| his paper addresses the problem of generating strong convex relaxations of Mixed Integer Quadratically Constrained Programming (MIQCP) problems. MIQCP problems are very difficult because they combine two kinds of non-convexities: integer variables and non-convex quadratic constraints. To produce strong relaxations of MIQCP problems, we use techniques from disjunctive programming and the lift-and-project methodology. In particular, we propose new methods for generating valid inequalities by using the equation Y = x x T . We use the concave constraint xx^T - Y psd to derive disjunctions of two types. The first ones are directly derived from the eigenvectors of the matrix Y − x x^T with positive eigenvalues, the second type of disjunctions are obtained by combining several eigenvectors in order to minimize the width of the disjunction. We also use the convex SDP constraint Y - xx^T psd to derive convex quadratic cuts and combine both approaches in a cutting plane algorithm. We present preliminary computational results to illustrate our findings. |
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| 1: | Tepper School of Business |
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Carnegie Mellon University |
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| 2: | Laboratoire d'informatique Fondamentale de Marseille (LIF) |
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CNRS : UMR6166 – Université de la Méditerranée - Aix-Marseille II – Université de Provence - Aix-Marseille I |
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| 3: | IBM Watson Research Center |
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IBM |
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| Subject | : | Computer Science/Operations Research Mathematics/Optimization and Control |
| hal-00421760, version 1 | |
| http://hal.archives-ouvertes.fr/hal-00421760 | |
| oai:hal.archives-ouvertes.fr:hal-00421760 | |
| From: Pierre Bonami | |
| Submitted on: Saturday, 3 October 2009 13:30:41 | |
| Updated on: Saturday, 3 October 2009 13:40:45 | |
