Robust optimality and duality for composite uncertain multiobjective optimization in Asplund spaces with its applications

TL;DR

This paper develops a comprehensive framework for analyzing uncertain multiobjective optimization problems in Asplund spaces, establishing optimality conditions, duality theories, and applications to complex composite problems using advanced variational analysis techniques.

Contribution

It introduces new optimality conditions, duality results, and solution existence criteria for nonsmooth, nonconvex uncertain multiobjective problems in Asplund spaces, with applications to practical composite problems.

Findings

Necessary optimality conditions via limiting subdifferential

Existence of weakly robust efficient solutions under pseudo-quasi convexity

Duality properties including weak, strong, and converse duality

Abstract

This article is devoted to investigate a nonsmooth/nonconvex uncertain multiobjective optimization problem with composition fields (CUP) for brevity) over arbitrary Asplund spaces. Employing some advanced techniques of variational analysis and generalized differentiation, we establish necessary optimality conditions for weakly robust efficient solutions of (CUP) in terms of the limiting subdifferential. Sufficient conditions for the existence of (weakly) robust efficient solutions to such a problem are also driven under the new concept of pseudo-quasi convexity for composite functions. We formulate a Mond-Weir-type robust dual problem to the primal problem (CUP), and explore weak, strong, and converse duality properties. In addition, the obtained results are applied to an approximate uncertain multiobjective problem and a composite uncertain multiobjective problem with linear operators.