On Finite Linear Systems Containing Strict Inequalities

Margarita M. L. Rodríguez () and José Vicente-Pérez ()
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Margarita M. L. Rodríguez: Universidad de Alicante
José Vicente-Pérez: Universidad de Alicante

Journal of Optimization Theory and Applications, 2017, vol. 173, issue 1, No 7, 154 pages

Abstract: Abstract This paper deals with linear systems containing finitely many weak and/or strict inequalities, whose solution sets are referred to as evenly convex polyhedral sets. 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 have been recently given by using the standard version for classical polyhedra. In this work, we provide a new dual tool 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.

Keywords: Linear systems; Strict inequalities; Polyhedra; Even convexity; Duality; 15A39; 49N15; 52B99 (search for similar items in EconPapers)
Date: 2017
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DOI: 10.1007/s10957-017-1079-2

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