  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.
