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Necessary conditions for weak efficiency for nonsmooth degenerate multiobjective optimization problems

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  • Elena Constantin

    (University of Pittsburgh at Johnstown)

Abstract

In this paper we give primal first and second-order necessary conditions for the existence of a local weak minimum for nonsmooth multiobjective optimization problems with inequality constraints and an arbitrary constraint set. For nonsmooth multiobjective problems with inequality and degenerate equality constraints, we present primal necessary conditions and Kuhn–Tucker type dual necessary conditions under a new constraint qualification. The effectiveness of our results is illustrated on some examples.

Suggested Citation

  • Elena Constantin, 2019. "Necessary conditions for weak efficiency for nonsmooth degenerate multiobjective optimization problems," Journal of Global Optimization, Springer, vol. 75(1), pages 111-129, September.
    • Handle: RePEc:spr:jglopt:v:75:y:2019:i:1:d:10.1007_s10898-019-00807-9
    DOI: 10.1007/s10898-019-00807-9
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    References listed on IDEAS

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    1. I. Ginchev & A. Guerraggio & M. Rocca, 2009. "Dini Set-Valued Directional Derivative in Locally Lipschitz Vector Optimization," Journal of Optimization Theory and Applications, Springer, vol. 143(1), pages 87-105, October.
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    8. Giorgio Giorgi & Bienvenido Jiménez & Vicente Novo, 2007. "Sufficient Optimality Conditions and Duality in Nonsmooth Multiobjective Optimization Problems under Generalized Convexity," Lecture Notes in Economics and Mathematical Systems, in: Generalized Convexity and Related Topics, pages 265-278, Springer.
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    Cited by:

    1. Elena Constantin, 2021. "Necessary conditions for weak minima and for strict minima of order two in nonsmooth constrained multiobjective optimization," Journal of Global Optimization, Springer, vol. 80(1), pages 177-193, May.
    2. Tran Su, 2024. "Optimality analysis for $$\epsilon $$ ϵ -quasi solutions of optimization problems via $$\epsilon $$ ϵ -upper convexificators: a dual approach," Journal of Global Optimization, Springer, vol. 90(3), pages 651-669, November.
    3. Elena Constantin, 2020. "Second-Order Optimality Conditions in Locally Lipschitz Inequality-Constrained Multiobjective Optimization," Journal of Optimization Theory and Applications, Springer, vol. 186(1), pages 50-67, July.

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