Relationship between nonsmooth vector optimization problem and vector variational inequalities using convexificators

In this article, we examine a nonsmooth vector optimization problem with locally Lipschitz approximately convex mappings in terms of the convexificator and provide some ideas for approximate effective solutions. Additionally, we define the relationship between the convexificator-based solutions of Stampacchia type vector variational inequalities ($VVI$) and the approximate efficient approximation convex function of nonsmooth vector optimization problems using the locally Lipschitz function. Furthermore, we provide a numerical example to demonstrate the veracity of our findings.