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may 2022 Optimality conditions for robust nonsmooth multiobjective optimization problems in Asplund spaces
Maryam Saadati, Oveisiha Morteza
Bull. Belg. Math. Soc. Simon Stevin 28(4): 579-601 (may 2022). DOI: 10.36045/j.bbms.210705

Abstract

We employ a fuzzy optimality condition for the Fréchet subdifferential and some advanced techniques of variational analysis such as formulae for the subdifferentials of an infinite family of nonsmooth functions and the coderivative scalarization to investigate robust optimality condition and robust duality for a nonsmooth/nonconvex multiobjective optimization problem dealing with uncertain constraints in arbitrary Asplund spaces. We establish necessary optimality conditions for weakly and properly robust efficient solutions of the problem in terms of the Mordukhovich subdifferentials of the related functions. Further, sufficient conditions for weakly and properly robust efficient solutions as well as for robust efficient solutions of the problem are provided by presenting new concepts of generalized. Finally, we formulate a Mond-Weir-type robust dual problem to the reference problem, and examine weak, strong, and converse duality relations between them under the pseudo convexity assumptions.

Citation

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Maryam Saadati. Oveisiha Morteza. "Optimality conditions for robust nonsmooth multiobjective optimization problems in Asplund spaces." Bull. Belg. Math. Soc. Simon Stevin 28 (4) 579 - 601, may 2022. https://doi.org/10.36045/j.bbms.210705

Information

Published: may 2022
First available in Project Euclid: 11 May 2022

Digital Object Identifier: 10.36045/j.bbms.210705

Subjects:
Primary: 65K10 , 90C29 , 90C46

Keywords: Duality , generalized convexity , limiting subdifferential , optimality conditions , Robust nonsmooth multiobjective optimization

Rights: Copyright © 2022 The Belgian Mathematical Society

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Vol.28 • No. 4 • may 2022
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