Lagrange duality of vector variational inequalities

In this paper, we investigate Lagrange dualities for a vector variational inequality problem. For a vector variational inequality problem with convex inclusion constraints, we develop an equivalent saddle point formulation via scalarization. For a vector variational inequality problem with linear constraints, we formulate a dual vector variational inequality via that of a linear multiobjective optimization problem and show that for a solution of a vector variational inequality problem, there is one corresponding solution for its dual. We give some examples to illustrate the results.