Asymptotic analysis for proximal-type methods in vector variational inequality problems

In this paper, we present a unified approach for studying vector variational inequality problems in finite dimensional spaces via asymptotic analysis. We introduce a class of weak normal mapping by virtue of the vector-valued indicator function. Then, we employ the obtained results to propose a class of proximal-type method to solve the vector variational inequality problems, carry out convergent analysis on the method and prove convergence of the generated sequence to a solution of the vector variational inequality problems under some mild conditions.