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On Tucker-Type Alternative Theorems and Necessary Optimality Conditions for Nonsmooth Multiobjective Optimization

Author

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  • Min Feng

    (Chongqing Jiaotong University)

  • Shengjie Li

    (Chongqing University)

  • Jie Wang

    (Chongqing University)

Abstract

This paper concentrates on necessary conditions for properly efficient solutions in nonsmooth multiobjective optimization problems. We first present a generalization of Tucker’s alternative theorem for conic nonlinear systems, provided that a closedness condition holds. Some sufficient conditions for the validity of such a closedness condition are given. As applications, under the weak Abadie regularity condition, we then establish the primal and the strong Karush/Kuhn–Tucker (dual) necessary optimality conditions for an efficient solution to be locally properly efficient in Borwein’s sense. The primal and the dual conditions are formulated as an equivalent pair by means of the Tucker-type alternative results. Finally we give an example to illustrate that Borwein’s locally properly efficient solution cannot be reduced to the only efficient one in the main results.

Suggested Citation

  • Min Feng & Shengjie Li & Jie Wang, 2022. "On Tucker-Type Alternative Theorems and Necessary Optimality Conditions for Nonsmooth Multiobjective Optimization," Journal of Optimization Theory and Applications, Springer, vol. 195(2), pages 480-503, November.
    • Handle: RePEc:spr:joptap:v:195:y:2022:i:2:d:10.1007_s10957-022-02092-1
    DOI: 10.1007/s10957-022-02092-1
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    References listed on IDEAS

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    7. Min Feng & Shengjie Li, 2018. "An approximate strong KKT condition for multiobjective optimization," TOP: An Official Journal of the Spanish Society of Statistics and Operations Research, Springer;Sociedad de Estadística e Investigación Operativa, vol. 26(3), pages 489-509, October.
    8. Min Feng & Shengjie Li, 2019. "Second-Order Strong Karush/Kuhn–Tucker Conditions for Proper Efficiencies in Multiobjective Optimization," Journal of Optimization Theory and Applications, Springer, vol. 181(3), pages 766-786, June.
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