Variational characterization of the contingent epiderivative

In this paper the existence of the contingent epiderivative of a set-valued map is studied from a variational perspective. We give a variational characterization of the ideal minimal of a weakly compact set. As a consequence we characterize the existence of the contingent epiderivative in terms of an associated family of variational systems. When a set-valued map takes values in Rn we show that these systems can be formulated in terms of the contingent epiderivatives of scalar set-valued maps. By applying these results we extend some existing theorems.