Epidifferentiability and hypodifferentiability of pseudoconvex maps in set-optimization problems

In this paper we study set-valued optimization problems with set-optimization criteria. With this aim we introduce two classes of pseudoconvex maps whose elements are epidifferentiable or hypodifferentiable. We establish optimality conditions in terms of the epiderivatives and hypoderivatives of associated maps of infima or suprema under pseudoconvexity conditions. Finally, by connecting set-optimization criteria with vector criterion, we apply these results in order to solve a vector optimization problem with constraints given by a set-valued map.