Optimality and Duality for Robust Optimization Problems Involving Intersection of Closed Sets

In this paper, we study a robust optimization problem whose constraints include nonsmooth and nonconvex functions and the intersection of closed sets. Using advanced variational analysis tools, we first provide necessary conditions for the optimality of the robust optimization problem. We then establish sufficient conditions for the optimality of the considered problem under the assumption of generalized convexity. In addition, we present a dual problem to the primal robust optimization problem and examine duality relations.