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

Nguyen Minh Tung ()
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Nguyen Minh Tung: University of Science

Journal of Optimization Theory and Applications, 2020, vol. 185, issue 2, No 8, 448-475

Abstract: 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.

Keywords: Higher-order optimality condition; Complementarity slackness; Henig-proper solution; Benson-proper solution; Positively proper solution; Contingent-type derivative; Constraint qualification; Directional metric subregularity; 90C29; 49J52; 90C46; 90C48 (search for similar items in EconPapers)
Date: 2020
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DOI: 10.1007/s10957-020-01654-5

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