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Structure and Weak Sharp Minimum of the Pareto Solution Set for Piecewise Linear Multiobjective Optimization

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Abstract

In this paper, the Pareto solution set of a piecewise linear multiobjective optimization problem in a normed space is shown to be the union of finitely many semiclosed polyhedra. If the problem is further assumed to be cone-convex, then it has the global weak sharp minimum property.

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Authors and Affiliations

  1. Department of Applied Mathematics, Hong Kong Polytechnic University, Hung Hom, Hong Kong

    X. Q. Yang

  2. Institute of Mathematics, Vietnamese Academy of Science and Technology, Hanoi, Vietnam

    N. D. Yen

Authors
  1. X. Q. Yang
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  2. N. D. Yen
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Corresponding author

Correspondence to X. Q. Yang.

Additional information

Communicated by F. Giannessi.

This work was partially supported by the Research Grants Council of Hong Kong (PolyU5303/05E) and National Foundation for Science & Technology Development (Vietnam).

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Yang, X.Q., Yen, N.D. Structure and Weak Sharp Minimum of the Pareto Solution Set for Piecewise Linear Multiobjective Optimization. J Optim Theory Appl 147, 113–124 (2010). https://doi.org/10.1007/s10957-010-9710-5

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  • DOI: https://doi.org/10.1007/s10957-010-9710-5

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