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Karush–Kuhn–Tucker Conditions in Set Optimization

Author

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  • Johannes Jahn

    (Universität Erlangen-Nürnberg)

Abstract

This paper investigates set optimization problems in finite dimensional spaces with the property that the images of the set-valued objective map are described by inequalities and equalities and that sets are compared with the set less order relation. For these problems new Karush–Kuhn–Tucker conditions are shown as necessary and sufficient optimality conditions. Optimality conditions without multiplier of the objective map are also presented. The usefulness of these results is demonstrated with a standard example.

Suggested Citation

  • Johannes Jahn, 2017. "Karush–Kuhn–Tucker Conditions in Set Optimization," Journal of Optimization Theory and Applications, Springer, vol. 172(3), pages 707-725, March.
    • Handle: RePEc:spr:joptap:v:172:y:2017:i:3:d:10.1007_s10957-017-1066-7
    DOI: 10.1007/s10957-017-1066-7
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    References listed on IDEAS

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    1. Johannes Jahn, 2015. "Vectorization in Set Optimization," Journal of Optimization Theory and Applications, Springer, vol. 167(3), pages 783-795, December.
    2. H. Th. Jongen & T. Möbert & K. Tammer, 1986. "On Iterated Minimization in Nonconvex Optimization," Mathematics of Operations Research, INFORMS, vol. 11(4), pages 679-691, November.
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    Cited by:

    1. Saeid Akhavan Bitaghsir & Ahmad Khonsari, 2019. "Modeling and improving the throughput of vehicular networks using cache enabled RSUs," Telecommunication Systems: Modelling, Analysis, Design and Management, Springer, vol. 70(3), pages 391-404, March.
    2. Lam Quoc Anh & Tran Quoc Duy & Dinh Vinh Hien & Daishi Kuroiwa & Narin Petrot, 2020. "Convergence of Solutions to Set Optimization Problems with the Set Less Order Relation," Journal of Optimization Theory and Applications, Springer, vol. 185(2), pages 416-432, May.
    3. Horng, Shih-Cheng & Lin, Shieh-Shing, 2019. "Bat algorithm assisted by ordinal optimization for solving discrete probabilistic bicriteria optimization problems," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 166(C), pages 346-364.

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