Optimality conditions for robust nonsmooth multiobjective optimization problems in Asplund spaces

Abstract

We employ a fuzzy optimality condition for the Fr´echet subdifferential and some ad-vanced 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.