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Piecewise Linear Multicriteria Programs: The Continuous Case and Its Discontinuous Generalization

Author

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  • Ya Ping Fang

    (Department of Mathematics, Sichuan University, Chengdu, Sichuan, China)

  • Kaiwen Meng

    (School of Economics and Management, Southwest Jiaotong University, Chengdu 610031, China)

  • Xiao Qi Yang

    (Department of Applied Mathematics, The Hong Kong Polytechnic University, Hung Hum, Kowloon, Hong Kong)

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 (infinity) risk measure and transaction costs and show that this algorithm can be improved by using an ideal point strategy.

Suggested Citation

  • 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.
    • Handle: RePEc:inm:oropre:v:60:y:2012:i:2:p:398-409
    DOI: 10.1287/opre.1110.1014
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    References listed on IDEAS

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    2. Siming Pan & Shaokai Lu & Kaiwen Meng & Shengkun Zhu, 2021. "Trade-Off Ratio Functions for Linear and Piecewise Linear Multi-objective Optimization Problems," Journal of Optimization Theory and Applications, Springer, vol. 188(2), pages 402-419, February.

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