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New Higher-Order Strong Karush–Kuhn–Tucker Conditions for Proper Solutions in Nonsmooth Optimization

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  • Nguyen Minh Tung

    (University of Science
    Vietnam National University)

Abstract

This paper considers higher-order necessary conditions for Henig-proper, positively proper and Benson-proper solutions. Under suitable constraint qualifications, our conditions are of the Karush–Kuhn–Tucker rule. The conditions include higher-order complementarity slackness for both the objective and the constraining maps. They are in a nonclassical form with a supremum expression on the right-hand side (instead of zero). Our results are new and improve the existing ones in the literature, even when applied to special cases of multiobjective single-valued optimization problems.

Suggested Citation

  • Nguyen Minh Tung, 2020. "New Higher-Order Strong Karush–Kuhn–Tucker Conditions for Proper Solutions in Nonsmooth Optimization," Journal of Optimization Theory and Applications, Springer, vol. 185(2), pages 448-475, May.
    • Handle: RePEc:spr:joptap:v:185:y:2020:i:2:d:10.1007_s10957-020-01654-5
    DOI: 10.1007/s10957-020-01654-5
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    References listed on IDEAS

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