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Normal regularity for the feasible set of semi-infinite multiobjective optimization problems with applications

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  • Thai Doan Chuong

    (University of New South Wales)

  • Do Sang Kim

    (Pukyong National University)

Abstract

We establish verifiable conditions for the feasible set of a nonsmooth semi-infinite multiobjective optimization problem to have the normal regularity (that is, the coincidence of the Fréchet normal cone and the limiting normal one) at a given point. In this way, both the Fréchet normal cone and the limiting normal one to the considered set are then computed via active constraint multipliers and limiting subdifferentials of the involved constraints. In order to achieve such goals, two classes of nonsmooth functions are introduced and exploited. Finally, the obtained results are applied to provide necessary optimality conditions for semi-infinite multiobjective optimization problems.

Suggested Citation

  • Thai Doan Chuong & Do Sang Kim, 2018. "Normal regularity for the feasible set of semi-infinite multiobjective optimization problems with applications," Annals of Operations Research, Springer, vol. 267(1), pages 81-99, August.
    • Handle: RePEc:spr:annopr:v:267:y:2018:i:1:d:10.1007_s10479-016-2337-7
    DOI: 10.1007/s10479-016-2337-7
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    References listed on IDEAS

    as
    1. Thai Doan Chuong & Do Sang Kim, 2016. "Hölder-Like Property and Metric Regularity of a Positive-Order for Implicit Multifunctions," Mathematics of Operations Research, INFORMS, vol. 41(2), pages 596-611, May.
    2. Thai Doan Chuong & Do Sang Kim, 2014. "Nonsmooth Semi-infinite Multiobjective Optimization Problems," Journal of Optimization Theory and Applications, Springer, vol. 160(3), pages 748-762, March.
    3. Thai Chuong & Do Kim, 2014. "Optimality conditions and duality in nonsmooth multiobjective optimization problems," Annals of Operations Research, Springer, vol. 217(1), pages 117-136, June.
    4. T. D. Chuong & J. C. Yao, 2010. "Generalized Clarke Epiderivatives of Parametric Vector Optimization Problems," Journal of Optimization Theory and Applications, Springer, vol. 146(1), pages 77-94, July.
    5. Boris S. Mordukhovich & T. T. A. Nghia, 2014. "Nonsmooth Cone-Constrained Optimization with Applications to Semi-Infinite Programming," Mathematics of Operations Research, INFORMS, vol. 39(2), pages 301-324, May.
    6. Thai Doan Chuong, 2013. "Derivatives of the Efficient Point Multifunction in Parametric Vector Optimization Problems," Journal of Optimization Theory and Applications, Springer, vol. 156(2), pages 247-265, February.
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    Cited by:

    1. Le Thanh Tung, 2022. "Karush–Kuhn–Tucker optimality conditions and duality for multiobjective semi-infinite programming with vanishing constraints," Annals of Operations Research, Springer, vol. 311(2), pages 1307-1334, April.
    2. Zhe Hong & Kwan Deok Bae & Do Sang Kim, 2022. "Minimax programming as a tool for studying robust multi-objective optimization problems," Annals of Operations Research, Springer, vol. 319(2), pages 1589-1606, December.

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