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On Finite Linear Systems Containing Strict Inequalities

Author

Listed:
  • Margarita M. L. Rodríguez

    (Universidad de Alicante)

  • José Vicente-Pérez

    (Universidad de Alicante)

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.

Suggested Citation

  • Margarita M. L. Rodríguez & José Vicente-Pérez, 2017. "On Finite Linear Systems Containing Strict Inequalities," Journal of Optimization Theory and Applications, Springer, vol. 173(1), pages 131-154, April.
    • Handle: RePEc:spr:joptap:v:173:y:2017:i:1:d:10.1007_s10957-017-1079-2
    DOI: 10.1007/s10957-017-1079-2
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    References listed on IDEAS

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    1. Ya Ping Fang & Nan Jing Huang & Xiao Qi Yang, 2012. "Local Smooth Representations of Parametric Semiclosed Polyhedra with Applications to Sensitivity in Piecewise Linear Programs," Journal of Optimization Theory and Applications, Springer, vol. 155(3), pages 810-839, December.
    2. Goberna, Miguel A. & Rodri'guez, Margarita M.L., 2006. "Analyzing linear systems containing strict inequalities via evenly convex hulls," European Journal of Operational Research, Elsevier, vol. 169(3), pages 1079-1095, March.
    3. Ya Ping Fang & Kaiwen Meng & Xiao Qi Yang, 2012. "Piecewise Linear Multicriteria Programs: The Continuous Case and Its Discontinuous Generalization," Operations Research, INFORMS, vol. 60(2), pages 398-409, April.
    4. Katta G. Murty, 2010. "Optimization for Decision Making," International Series in Operations Research and Management Science, Springer, number 978-1-4419-1291-6, April.
    5. X. Q. Yang & N. D. Yen, 2010. "Structure and Weak Sharp Minimum of the Pareto Solution Set for Piecewise Linear Multiobjective Optimization," Journal of Optimization Theory and Applications, Springer, vol. 147(1), pages 113-124, October.
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