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

Ya Ping Fang (), Nan Jing Huang () and Xiao Qi Yang ()
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Ya Ping Fang: Sichuan University
Nan Jing Huang: Sichuan University
Xiao Qi Yang: The Hong Kong Polytechnic University

Journal of Optimization Theory and Applications, 2012, vol. 155, issue 3, No 5, 810-839

Abstract: 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.

Keywords: Parametric semiclosed polyhedra; Smooth representation; Piecewise linear program; Sensitivity (search for similar items in EconPapers)
Date: 2012
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DOI: 10.1007/s10957-012-0089-3

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