Piecewise linear multicriteria programs: The continuous case and its discontinuous generalization

Ya Ping Fang, Kaiwen Meng, Xiaoqi Yang

Research output: Journal article publicationJournal articleAcademic researchpeer-review

17 Citations (Scopus)

Abstract

In this paper we study piecewise linear multicriteria programs, that is, multicriteria programs with either a continuous or discontinuous piecewise linear objective function and a polyhedron set constraint. We obtain an algebraic representation of a semi-closed polyhedron and apply it to show that the image of a semi-closed polyhedron under a continuous linear function is always one semi-closed polyhedron. We establish that the (weak) Pareto solution/point set of a piecewise linear multicriteria program is the union of finitely many semi-closed polyhedra. We propose an algorithm for finding the Pareto point set of a continuous piecewise linear bi-criteria program and generalize it to the discontinuous case. We apply our algorithm to solve the discontinuous bi-criteria portfolio selection problem with an l∞risk measure and transaction costs and show that this algorithm can be improved by using an ideal point strategy.
Original languageEnglish
Pages (from-to)398-409
Number of pages12
JournalOperations Research
Volume60
Issue number2
DOIs
Publication statusPublished - 1 Mar 2012

Keywords

  • Algorithm
  • Bi-criteria program
  • Multicriteria program
  • Piecewise linear function
  • The structure of (weak) Pareto solution set

ASJC Scopus subject areas

  • Computer Science Applications
  • Management Science and Operations Research

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