Generalized invexity of nonsmooth functions

In this paper, the concepts of weak invexity and weak quasi invexity are introduced and the relations among several kinds of generalized invexity are studied for nonsmooth functions by means of the properties of limiting subdifferentials. In addition, the relations between generalized invexity of a nonsmooth function and generalized invariant monotonicity of its limiting subdifferential mapping are researched. Our results here are an extension and generalization of those presented by M. Soleimani-damaneh.