On Weak Subdifferential and Augmented Normal Cone

Abstract

In this paper, we study augmented normal cone and investigate relation between weak sub-differential and augmented normal cone. we define augmented normal cone via weak subdifferential and vice versa. The necessary condition for having the global maximum is given in the paper. We find the preliminary properties of augmented normal cones including investigating them for Fréchet differentiable functions. In the sequel, some properties of Weak subdifferential and Fréchet subdifferentil are con-sidered. It is also compared optimality condition via weak subifferential and optimality condition via Fréchet subifferential.