On Relationships Between Vector Variational Inequality and Nonsmooth Vector Optimization Problems via Strict Minimizers

Abstract

This paper deals with the relations between vector variational inequality problems and nonsmooth vector optimization problems using the concepts of efficient and strict minimizers of order m in terms of Clarke subdifferential. The Gordan’s theorem of alternative is employed to identify the vector critical points, the strict minimizers of order m and the solutions of the weak vector variational inequality problems under generalized strong convexity assumptions. The results presented in this paper are more general than those existing in the literature. In particular, the results of the paper extend and unify some earlier results of Bhatia [6], Giannessi [14], Lee and Lee [22], Osuna-Gomez et al. [34], and Yang [38] to the nonsmooth case as well as to a more general class of functions.