Radial epiderivatives and set-valued optimization

Abstract

In this article we study some important properties of the radial epiderivatives for single-valued and set-valued maps. The relationships between this kind of a derivative and weak subdifferentials and directional derivatives in the single-valued non-convex case has been established. For optimization problems with a single-valued and a set-valued objective function, necessary and sufficient optimality conditions based on the concept of the radial epiderivatives are proved without convexity conditions.