An inexact LQP alternating direction method for solving a class of structured variational inequalities

In this paper, we present an inexact alternating direction method. Each iteration of the proposed method contains a prediction and a correction, the predictor is obtained via solving the logarithmic-quadratic proximal (LQP) system approximately under significantly relaxed accuracy criterion and the new iterate is computed directly by an explicit formula derived from the original LQP method. Under certain conditions, the global convergence of the proposed method is proved.