G-α-preinvex functions and non-smooth vector optimization problems

Abstract

In this paper, we proposed the non-smooth G-?-preinvexity by generalizing ?-invexity and G-preinvexity, and discussed some solution properties about non-smooth vector optimization problems and vector variational-like inequality problems under the condition of non-smooth G-?-preinvexity. Moreover, we also proved that the vector critical points, the weakly efficient points and the solutions of the non-smooth weak vector variational-like inequality problem are equivalent under non-smooth pseudo-G-?-preinvexity assumptions.