On Vector Variational- Like Inequalities and Vector Optimization Problems Using Convexificators

Abstract

In this paper, we formulate the relationship between the quasi efficient solution of nonsmooth vector optimization problems involving the locally Lipschitz function and the convexificator-based solutions of Stampacchia type vector variational-like inequality problems by using an approximate invex function. We also identify under approximate pseudoinvexity assumptions the weakly quasi efficient points, the vector critical points, and the solutions of the nonsmooth weak vector variational-like inequality problems are equal. Our newly proved results generalize some well-known results in the literature.