On Weak Subdifferential and Augmented Normal Cone

Ali Farajzadeh, Parisa Cheraghi, Suthep Suantai

Abstract

In this paper, we study augmented normal cone . We investigaterelation between weak subdifferential and augmented normal cone. We try todene augmented normal cone via weak subdifferential and vice versa. The nec-essary condition for having the global maximum states in this paper. We ndthe preliminary properties of augmented normal cones. Also augmented normalcones investigated for Frechet differentiable functions.In the sequel , some proper-ties of weak subifferential and Frechet subdifferential are considered. Investigationof relation between weak subifferential and Frechet subdifferential is an idea ofthis paper. It is also compared optimality condition via weak subifferential andoptimality condition via Frechet subdifferential.