Approximate solutions for robust multiobjective optimization programming in Asplund spaces

In this paper, we study a nonsmooth/nonconvex multiobjective optimization problem with uncertain constraints in arbitrary Asplund spaces. We first provide necessary optimality condition in a fuzzy form for approximate weakly robust efficient solutions and then establish necessary optimality theorem...

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Bibliographic Details
Published in:Optimization 2024-02, Vol.73 (2), p.329-357
Main Authors: Saadati, Maryam, Oveisiha, Morteza
Format: Article
Language:English
Subjects:
Approximate solutions
Convexity
generalized convexity
limiting subdifferential
Multiple objective analysis
optimality conditions
Optimization
robust multiobjective optimization
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Summary:In this paper, we study a nonsmooth/nonconvex multiobjective optimization problem with uncertain constraints in arbitrary Asplund spaces. We first provide necessary optimality condition in a fuzzy form for approximate weakly robust efficient solutions and then establish necessary optimality theorem for approximate weakly robust quasi-efficient solutions of the problem in the sense of the limiting subdifferential by exploiting a fuzzy optimality condition in terms of the Fréchet subdifferential. Sufficient conditions for approximate (weakly) robust quasi-efficient solutions to such a problem are also driven under the new concept of generalized pseudo convex functions. Finally, we address an approximate Mond-Weir-type dual robust problem to the reference problem and explore weak, strong, and converse duality properties under assumptions of pseudo convexity.
ISSN:0233-1934
1029-4945
DOI:10.1080/02331934.2022.2105214