Optimality Conditions and Duality for Robust Nonsmooth Multiobjective Optimization Problems with Constraints

Jiawei Chen (), Elisabeth Köbis () and Jen-Chih Yao ()
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Jiawei Chen: Southwest University
Elisabeth Köbis: Halle-Wittenberg
Jen-Chih Yao: China Medical University

Journal of Optimization Theory and Applications, 2019, vol. 181, issue 2, No 3, 436 pages

Abstract: Abstract In this paper, we investigate a robust nonsmooth multiobjective optimization problem related to a multiobjective optimization with data uncertainty. We firstly introduce two kinds of generalized convex functions, which are not necessary to be convex. Robust necessary optimality conditions for weakly robust efficient solutions and properly robust efficient solutions of the problem are established by a generalized alternative theorem and the robust constraint qualification. Further, robust sufficient optimality conditions for weakly robust efficient solutions and properly robust efficient solutions of the problem are also derived. The Mond–Weir-type dual problem and Wolfe-type dual problem are formulated. Finally, we obtain the weak, strong and converse robust duality results between the primal one and its dual problems under the generalized convexity assumptions.

Keywords: Robust nonsmooth multiobjective optimization; Uncertain nonsmooth multiobjective optimization; Robust optimality conditions; Robust duality; 65K10; 90C25 (search for similar items in EconPapers)
Date: 2019
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Citations: View citations in EconPapers (13)

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DOI: 10.1007/s10957-018-1437-8

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