{"125821":{"#nid":"125821","#data":{"type":"event","title":"ACO\/DOS Seminar","body":[{"value":"\u003Cp\u003E\u003Cstrong\u003ETitle:\u003C\/strong\u003E\u0026nbsp;\u0026nbsp; Some properties of convex hulls of mixed integer points contained in general convex sets\u003C\/p\u003E\u003Cp\u003E\u003Cstrong\u003ESpeaker:\u003C\/strong\u003E\u0026nbsp; Diego Mor\u00e1n, ISyE - Georgia Tech\u003C\/p\u003E\u003Cp\u003E\u003Cstrong\u003EAbstract:\u003C\/strong\u003E\u003C\/p\u003E\u003Cp\u003EA mixed integer point is a vector in $\\mathbb{R}^n$ whose first $n_1$ coordinates are integer. We present necessary and sufficient conditions for the convex hull of mixed integer points contained in a general convex set to be closed. This leads to useful results for special classes of convex sets such as pointed cones and strictly convex sets.\u0026nbsp;\u003C\/p\u003E\u003Cp\u003EFurthermore, by using these results, we show that there exists a polynomial time algorithm to check the closedness of the convex hull of the mixed integer points contained in the feasible region of a second order conic programming problem, for the special case this region is defined by just one Lorentz cone and one rational matrix.\u003C\/p\u003E\u003Cp\u003EThis is joint work with Santanu Dey.\u003C\/p\u003E\u003Cp\u003EPizza and\u0026nbsp;refreshments will be served. \u003Cbr \/\u003E\u003C\/p\u003E","summary":null,"format":"limited_html"}],"field_subtitle":"","field_summary":"","field_summary_sentence":[{"value":"ACO\/DOS Seminar"}],"uid":"27187","created_gmt":"2012-04-24 08:24:10","changed_gmt":"2016-10-08 01:54:38","author":"Anita Race","boilerplate_text":"","field_publication":"","field_article_url":"","field_event_time":{"event_time_start":"2012-04-25T17:00:00-04:00","event_time_end":"2012-04-25T18:00:00-04:00","event_time_end_last":"2012-04-25T18:00:00-04:00","gmt_time_start":"2012-04-25 21:00:00","gmt_time_end":"2012-04-25 22:00:00","gmt_time_end_last":"2012-04-25 22:00:00","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\u003ERodolfo Carvajal\u003C\/p\u003E\u003Cp\u003E\u003Ca href=\u0022mailto:rocarvaj@gatech.edu\u0022\u003Erocarvaj@gatech.edu\u003C\/a\u003E\u003C\/p\u003E","format":"limited_html"}],"email":[],"slides":[],"orientation":[],"userdata":""}}}