Abstract:  The subject of study is a semi-infinite optimization problem in Banach spaces, where both the objective functional and the constraint operator are compositions of convex non-smooth mappings and differentiable mappings. Necessary and sufficient conditions of optimality conditions for this problem will be presented. Our results extend and generalize the theory of semi-infinite and composite optimization in vector spaces. We apply the results to non-convex stochastic optimization problems with stochastic dominance constraints, generalizing our earlier results.

This is a joint work with Andrzej Ruszczynski, Rutgers University, Piscataway, NJ08854, USA.