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Nonsmooth Multiobjective Problems and Generalized Vector Variational Inequalities Using Quasi-Efficiency

Author

Listed:
  • M. Golestani

    (Fasa University)

  • H. Sadeghi

    (Shahid Chamran University of Ahvaz)

  • Y. Tavan

    (Shahid Chamran University of Ahvaz)

Abstract

In this paper, a multiobjective problem with a feasible set defined by inequality, equality and set constraints is considered, where the objective and constraint functions are locally Lipschitz. Here, a generalized Stampacchia vector variational inequality is formulated as a tool to characterize quasi- or weak quasi-efficient points. By using two new classes of generalized convexity functions, under suitable constraint qualifications, the equivalence between Kuhn–Tucker vector critical points, solutions to the multiobjective problem and solutions to the generalized Stampacchia vector variational inequality in both weak and strong forms will be proved.

Suggested Citation

  • M. Golestani & H. Sadeghi & Y. Tavan, 2018. "Nonsmooth Multiobjective Problems and Generalized Vector Variational Inequalities Using Quasi-Efficiency," Journal of Optimization Theory and Applications, Springer, vol. 179(3), pages 896-916, December.
    • Handle: RePEc:spr:joptap:v:179:y:2018:i:3:d:10.1007_s10957-017-1179-z
    DOI: 10.1007/s10957-017-1179-z
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    References listed on IDEAS

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