Optimality conditions for robust nonsmooth multiobjective optimization problems in Asplund spaces

TL;DR

This paper develops necessary and sufficient optimality conditions for robust multiobjective optimization problems with nonsmooth, nonconvex features in Asplund spaces, using advanced variational analysis techniques.

Contribution

It introduces new optimality conditions and duality results for robust nonsmooth multiobjective problems in general Asplund spaces, extending existing theory.

Findings

Established necessary optimality conditions using Mordukhovich subdifferentials.

Provided sufficient conditions based on generalized convexity concepts.

Formulated a Mond-Weir-type robust dual problem and analyzed duality relations.

Abstract

We employ a fuzzy optimality condition for the Frechet 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 convexity. 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.