Approximate solutions for robust multiobjective optimization programming in Asplund spaces

TL;DR

This paper develops necessary and sufficient optimality conditions for approximate robust solutions in complex multiobjective optimization problems within Asplund spaces, using fuzzy and subdifferential techniques.

Contribution

It introduces new optimality conditions and duality results for nonsmooth, nonconvex multiobjective problems with uncertainty in Asplund spaces, expanding theoretical understanding.

Findings

Established fuzzy optimality conditions for approximate solutions

Derived duality properties under pseudo convexity assumptions

Extended the theory to nonsmooth, nonconvex multiobjective problems

Abstract

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 Frechet 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.