Optimality conditions for robust nonsmooth multiobjective optimization problems in Asplund spaces

We employ a fuzzy optimality condition for the Fre ' chet 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 ro-bust efficient solutions of the problem in terms of the Mordukhovich subd-ifferentials of the related functions. Further, sufficient conditions for weakly and properly robust efficient solutions as well as for robust efficient solu-tions 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 rela-tions between them under the pseudo convexity assumptions.