Contingent epiderivatives and set-valued optimization

In this paper we introduce the concept of the contingent epiderivative for a set-valued map which modifies a notion introduced by Aubin as upper contingent derivative. It is shown that this kind of a derivative has important properties and is one possible generalization of directional derivatives in the single-valued convex case. For optimization problems with a set-valued objective function optimality conditions based on the concept of the contingent epiderivative are proved which are necessary and sufficient under suitable assumptions.