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Local Smooth Representations of Parametric Semiclosed Polyhedra with Applications to Sensitivity in Piecewise Linear Programs

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  • Ya Ping Fang

    (Sichuan University)

  • Nan Jing Huang

    (Sichuan University)

  • Xiao Qi Yang

    (The Hong Kong Polytechnic University)

Abstract

In this paper, we establish the equivalence between the half-space representation and the vertex representation of a smooth parametric semiclosed polyhedron. By virtue of the smooth representation result, we prove that the solution set of a smooth parametric piecewise linear program can be locally represented as a finite union of parametric semiclosed polyhedra generated by finite smooth functions. As consequences, we prove that the corresponding marginal function is differentiable and the solution map admits a differentiable selection.

Suggested Citation

  • 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.
    • Handle: RePEc:spr:joptap:v:155:y:2012:i:3:d:10.1007_s10957-012-0089-3
    DOI: 10.1007/s10957-012-0089-3
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    References listed on IDEAS

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    1. Darinka Dentcheva & Andrzej Ruszczynski, 2004. "Optimization Under First Order Stochastic Dominance Constraints," GE, Growth, Math methods 0403002, University Library of Munich, Germany, revised 07 Aug 2005.
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    4. 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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    Cited by:

    1. 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.

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