Generalized Vector Variational-Like Inequalities

Abstract

In this paper, we consider different types of generalized
vector variational-like inequalities and study the relationships between
their solutions. We study the general forms of Stampacchia and Minty
type vector variational inequalities for bifunctions and establish the existence
of their solutions in the setting of topological vector spaces.
We extend these vector variational inequalities for the Clarke’s subdifferential
of non-differentiable locally Lipschitz functions and prove the
existence of their solutions. As applications, we establish some existence
results for a solution of the vector optimization problem by using
Stampacchia and Minty type vector variational inequalities.