{"73259":{"#nid":"73259","#data":{"type":"event","title":"OR Colloquium - Convexification Techniques for Linear Complementarity Constraints","body":[{"value":"\u003Cp\u003ETITLE: Convexification Techniques for Linear Complementarity Constraints\n\n\u003C\/p\u003E\u003Cp\u003ESPEAKER:\u0026nbsp; Jean-Philippe Richard\u003C\/p\u003E\u003Cp\u003EABSTRACT:\u003C\/p\u003E\u003Cp\u003EIn this talk, we discuss strong convex relaxations of mathematical\nprograms with complementarity constraints (MPCCs). MPCCs have numerous\npractical applications in business, engineering, and economics because\ncomplementarity conditions arise in the mathematical modeling of games and\nequilibria. and because nonlinear programs in which constraint functions\nare differentiable can be reformulated in a higher dimensional space using\n\noptimality conditions.\u003C\/p\u003E\u003Cp\u003E\n\n\n\nWe first describe a convexification technique for linear programs with\nlinear complementarity constraints that generalizes the\nreformulation-linearization technique of Sherali and Adams and has similar\nconvergence properties. We then consider certain complementarity problems\nappearing in KKT systems. For such problems, we show that all nontrivial\nfacet-defining inequalities can be obtained through a simple procedure\nthat aggregates constraints and use McCormick relaxations of bilinear\nterms. Finally, we discuss the problem of generating strong cutting\nplanes, in the space of the original variables,  from the optimal simplex\ntableaux of the LP relaxation of the problem. We discuss the geometry of\nthe corresponding sets and compare the strength of the cuts thus obtained\nwith respect to RLT, disjunctive, and other approaches in the literature.\n\u003C\/p\u003E\u003Cp\u003E\n\n\nThis talk is based on joint work with Trang Nguyen (UF) and Mohit\nTawarmalani (Purdue).\n\u003C\/p\u003E\u003Cp\u003E\n\u003Cstrong\u003EBio:\u003C\/strong\u003E\n\nJean-Philippe Richard is an associate professor in the Department of\nIndustrial and Systems Engineering at the University of Florida . After\nreceving a bachelor in Applied Mathematics Engineering at Universite\nCatholique de Louvain in Louvain-La-Neuve, Belgium, he came to study at\nthe Georgia Institute of Technology where he received a Phd in Algorithms,\nCombinatorics and Optimization. His current research interests include the\nuse of polyhedral and convex analysis techniques for the derivation of\nstrong convex relaxations of mixed integer linear and nonlinear programs.\nHe is also currently working with CSX on large-scale optimization problems\narising in railroads and with SAS-OR on computational issues associated\nwith the solution of integer programs.\n\u003C\/p\u003E","summary":null,"format":"limited_html"}],"field_subtitle":"","field_summary":"","field_summary_sentence":[{"value":"Convexification Techniques for Linear Complementarity Constraints"}],"uid":"27187","created_gmt":"2011-11-30 11:37:02","changed_gmt":"2016-10-08 01:56:45","author":"Anita Race","boilerplate_text":"","field_publication":"","field_article_url":"","field_event_time":{"event_time_start":"2011-12-06T11:00:00-05:00","event_time_end":"2011-12-06T12:30:00-05:00","event_time_end_last":"2011-12-06T12:30:00-05:00","gmt_time_start":"2011-12-06 16:00:00","gmt_time_end":"2011-12-06 17:30:00","gmt_time_end_last":"2011-12-06 17:30:00","rrule":null,"timezone":"America\/New_York"},"extras":[],"groups":[{"id":"1242","name":"School of Industrial and Systems Engineering (ISYE)"}],"categories":[],"keywords":[],"core_research_areas":[],"news_room_topics":[],"event_categories":[{"id":"1795","name":"Seminar\/Lecture\/Colloquium"}],"invited_audience":[],"affiliations":[],"classification":[],"areas_of_expertise":[],"news_and_recent_appearances":[],"phone":[],"contact":[{"value":"\u003Cp\u003ESantanu Dey\u003C\/p\u003E","format":"limited_html"}],"email":[],"slides":[],"orientation":[],"userdata":""}}}