A proximal decomposition algorithm for variational inequality problems

Abstract

In this paper, we propose a new decomposition algorithm for solving monotone variational inequality problems with linear constraints. The algorithm utilizes the problem's structure conductive to decomposition. At each iteration, the algorithm solves a system of nonlinear equations, which is structurally much easier to solve than variational inequality problems, the subproblems of classical decomposition methods, and then performs a projection step to update the multipliers. We allow to solve the subproblems approximately and we prove that under mild assumptions on the problem's data, the algorithm is globally convergent. We also report some preliminary computational results, which show that the algorithm is encouraging.