Some relationships among gw-subdifferential, directional derivative and radial epiderivative for nonconvex vector functions

Abstract

In this work, we give some characterizations of gw-subdifferentiability of a vector-valued function by using its directional derivative and radial epiderivative. Moreover, under some assumptions, we proved that the directional derivative and radial epiderivative of a vector-valued function are the elements of the supremum set of gw-subgradients of it. Finally, without any convexity assumption, we proved that the epigraph of contingent derivative of a set valued map is included in the epigraph of contingent epiderivative of this set-valued map.

Keywords:

• generalized weak subdifferential
• radial epiderivative
• contingent derivative
• contingent epiderivative
• directional derivative
• non-convex optimization

AMS Subject Classifications:

• 26A24
• 28B99
• 49J52
• 65K10