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Unified Robust Necessary Optimality Conditions for Nonconvex Nonsmooth Uncertain Multiobjective Optimization

Author

Listed:
  • Jie Wang

    (Chongqing University)

  • Shengjie Li

    (Chongqing University)

  • Min Feng

    (Chongqing Jiaotong University)

Abstract

This paper is concerned with nonconvex nonsmooth uncertain multiobjective optimization problems, in which the decision variable of both objective and constraint functions is defined on Banach space while uncertain parameters are defined on arbitrary nonempty (may not be compact) sets. We employ the Stone–C̆ech compactification of uncertainty sets and the upper semicontinuous regularization of original functions with respect to uncertain parameters, giving rise to unified robust necessary optimality conditions for the local robust weakly efficient solution of the considered problem. Moreover, we derive weak and strong KKT robust necessary conditions via the constraint qualification and the regularity condition, respectively. Several examples are provided to illustrate the validity of our results.

Suggested Citation

  • Jie Wang & Shengjie Li & Min Feng, 2022. "Unified Robust Necessary Optimality Conditions for Nonconvex Nonsmooth Uncertain Multiobjective Optimization," Journal of Optimization Theory and Applications, Springer, vol. 195(1), pages 226-248, October.
    • Handle: RePEc:spr:joptap:v:195:y:2022:i:1:d:10.1007_s10957-022-02075-2
    DOI: 10.1007/s10957-022-02075-2
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    References listed on IDEAS

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    7. Jiawei Chen & Suliman Al-Homidan & Qamrul Hasan Ansari & Jun Li & Yibing Lv, 2021. "Robust Necessary Optimality Conditions for Nondifferentiable Complex Fractional Programming with Uncertain Data," Journal of Optimization Theory and Applications, Springer, vol. 189(1), pages 221-243, April.
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