An Inexact Proximal Alternating Directions Method For Structured Variational Inequalities∗

In this paper we propose an appealing inexact proximal alternating directions method (abbreviated as In-PADM) for solving a class of monotone variational inequalities with certain special structure, and this structure under consideration is common in practice. We prove convergence of In-PADM method while the inexact term is arbitrary but satisfied some suitable conditions. For solving the variational inequalities with the special structure under consideration, we prove the proximal point term in one of the variational inequalities can be taken out, while convergence of the proposed method is preserved. And to do in this way, some advantages are provided in the implementation of In-PADM method. Numerical tests on Compressed Sensor problem show applicability and availability of In-PADM method.