Abstract: This paper is devoted to the study of the relations between vector variational inequality and nonsmooth multi-objective optimization in the sense of strict minimizers of higher order. We firstly introduce an extension of higher-order strong pseudoconvexity for Lipschitz functions, termed higher-order strongly pseudoconvex functions of type I, and some examples are presented in the support of this generalization. Then, we identify the strict minimizers of higher order, the vector critical points and the solutions of the weak vector variational inequality problem under the higher-order strong pseudoconvexity of type I hypothesis. It is our understanding that such results have not been established till now.

Key words: multi-objective optimization, strict minimizer of higher order, vector variational inequality, strong convexity