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Exact Penalty and Optimality Condition for Nonseparable Continuous Piecewise Linear Programming

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  • Xiaolin Huang

    (Tsinghua University)

  • Jun Xu

    (Tsinghua University)

  • Shuning Wang

    (Tsinghua University)

Abstract

Utilizing compact representations for continuous piecewise linear functions, this paper discusses some theoretical properties for nonseparable continuous piecewise linear programming. The existence of exact penalty for continuous piecewise linear programming is proved, which allows us to concentrate on unconstrained problems. For unconstrained problems, we give a sufficient and necessary local optimality condition, which is based on a model with universal representation capability and hence applicable to arbitrary continuous piecewise linear programming. From the gained optimality condition, an algorithm is proposed and evaluated by numerical experiments, where the theoretical properties are illustrated as well.

Suggested Citation

  • Xiaolin Huang & Jun Xu & Shuning Wang, 2012. "Exact Penalty and Optimality Condition for Nonseparable Continuous Piecewise Linear Programming," Journal of Optimization Theory and Applications, Springer, vol. 155(1), pages 145-164, October.
    • Handle: RePEc:spr:joptap:v:155:y:2012:i:1:d:10.1007_s10957-012-0032-7
    DOI: 10.1007/s10957-012-0032-7
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    References listed on IDEAS

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    4. Keely L. Croxton & Bernard Gendron & Thomas L. Magnanti, 2003. "A Comparison of Mixed-Integer Programming Models for Nonconvex Piecewise Linear Cost Minimization Problems," Management Science, INFORMS, vol. 49(9), pages 1268-1273, September.
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