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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This research was partially supported by MINECO of Spain and ERDF of EU, Grants MTM2014-59179-C2-1-P and ECO2016-77200-P.
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Communicated by Nicolas Hadjisavvas.
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Rodríguez, M.M.L., Vicente-Pérez, J. On Finite Linear Systems Containing Strict Inequalities. J Optim Theory Appl 173, 131–154 (2017). https://doi.org/10.1007/s10957-017-1079-2
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DOI: https://doi.org/10.1007/s10957-017-1079-2