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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Bibliographic Details
Published in:Journal of optimization theory and applications Vol. 181; no. 2; pp. 411 - 436
Main Authors: Chen, Jiawei, Köbis, Elisabeth, Yao, Jen-Chih
Format: Journal Article
Language:English
Published: New York Springer US 01.05.2019
Springer Nature B.V
Subjects:
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
Online Access:Get full text
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Summary: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.
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ISSN:0022-3239
1573-2878
DOI:10.1007/s10957-018-1437-8