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The structure of weak Pareto solution sets in piecewise linear multiobjective optimization in normed spaces

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Abstract

In general normed spaces, we consider a multiobjective piecewise linear optimization problem with the ordering cone being convex and having a nonempty interior. We establish that the weak Pareto optimal solution set of such a problem is the union of finitely many polyhedra and that this set is also arcwise connected under the cone convexity assumption of the objective function. Moreover, we provide necessary and sufficient conditions about the existence of weak (sharp) Pareto solutions.

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Authors and Affiliations

  1. Department of Mathematics, Yunnan University, Kunming, 650091, China

    XiYin Zheng

  2. Department of Applied Mathematics, the Hong Kong Polytechnic University, Hung Hum, Kowloon, Hong Kong, China

    XiaoQi Yang

Authors
  1. XiYin Zheng
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  2. XiaoQi Yang
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Correspondence to XiYin Zheng.

Additional information

This work was supported by the National Natural Science Foundation of China (Grant No. 10761012), the Natural Science Foundation of Yunnan Province, China (Grant No. 2003A002M) and the Research Grants Council of Hong Kong (Grant No. B-Q771)

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Zheng, X., Yang, X. The structure of weak Pareto solution sets in piecewise linear multiobjective optimization in normed spaces. Sci. China Ser. A-Math. 51, 1243–1256 (2008). https://doi.org/10.1007/s11425-008-0021-3

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  • DOI: https://doi.org/10.1007/s11425-008-0021-3

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