On Finite Linear Systems Containing Strict Inequalities |
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Authors: | Margarita M L Rodríguez José Vicente-Pérez |
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Institution: | 1.Departamento de Matemáticas,Universidad de Alicante,Alicante,Spain;2.Departamento de Fundamentos del Análisis Económico,Universidad de Alicante,Alicante,Spain |
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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. |
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