The classical Motzkin theorem states that every (closed and convex) polyhedron is the Minkowski sum of a convex hull of finitely many points and a finitely generated cone. In this sense, similar representations for evenly convex polyhedra (the solution sets of linear systems containing finitely many weak and/or strict inequalities) have been recently given in the literature by employing the standard version for classical polyhedra. In this talk, we show a new dual cone that completely characterizes finite linear systems containing strict inequalities and it constitutes the key for obtaining a generalization of Motzkin theorem for evenly convex polyhedra.
Having completed two degrees in Mathematics and Statistics, José got his Ph.D. in Mathematics in 2011 from the University of Murcia (Spain) supported by a research fellowship from the Ministry of Education in Spain. He started his professional career in Pamplona (world-famous by the Running of the Bulls) at the Public University of Navarre. In October 2012 he became a Postdoctoral Research Associate at the School of Mathematics and Statistics within the University of New South Wales (Australia) under the direction of Professor V. Jeyakumar. In September 2013 he moved to Madrid as a visiting professor in the Department of Economics at the Carlos III University of Madrid. Since October 2015, he has been a lecturer in the University of Alicante. Jose is passionate about Convex Analysis and its applications to Optimization.
Linear systems; Strict inequalities; Polyhedra; Even convexity; Duality.