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

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...

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Vydáno v:Journal of optimization theory and applications Ročník 181; číslo 2; s. 411 - 436
Hlavní autoři: Chen, Jiawei, Köbis, Elisabeth, Yao, Jen-Chih
Médium: Journal Article
Jazyk:angličtina
Vydáno: New York Springer US 01.05.2019
Springer Nature B.V
Témata:
Applications of Mathematics
Calculus of Variations and Optimal Control; Optimization
Convexity
Economic models
Engineering
Mathematical programming
Mathematics
Mathematics and Statistics
Multiple objective analysis
Nonlinear programming
Operations Research/Decision Theory
Optimization
Robustness
Theory of Computation
65K10
Robust optimality conditions
Robust nonsmooth multiobjective optimization
Robust duality
90C25
Uncertain nonsmooth multiobjective optimization
ISSN:0022-3239, 1573-2878
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Popis
Shrnutí: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.
Bibliografie:ObjectType-Article-1
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ObjectType-Feature-2
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ISSN:0022-3239
1573-2878
DOI:10.1007/s10957-018-1437-8