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

Ya Ping Fang, Nan Jing Huang, Xiaoqi Yang

Research output: Journal article publicationJournal articleAcademic researchpeer-review

4 Citations (Scopus)


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.
Original languageEnglish
Pages (from-to)810-839
Number of pages30
JournalJournal of Optimization Theory and Applications
Issue number3
Publication statusPublished - 1 Dec 2012


  • Parametric semiclosed polyhedra
  • Piecewise linear program
  • Sensitivity
  • Smooth representation

ASJC Scopus subject areas

  • Control and Optimization
  • Management Science and Operations Research
  • Applied Mathematics

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