On alternating direction method for solving variational inequality problems with separable structure

We present an alternating direction scheme for the separable constrained convex programming problem. The predictor is obtained via solving two sub-variational inequalities in a parallel wise at each iteration. The new iterate is obtained by a projection type method along a new descent direction. The new direction is obtained by combining the descent directions using by He [B.-S. He, Comput. Optim. Appl., 42 (2009), 195–212] and Jiang and Yuan [Z.-K. Jiang, X.-M. Yuan, J. Optim. Theory Appl., 145 (2010), 311–323]. Global convergence of the proposed method is proved under certain assumptions. We also report some numerical results to illustrate the efficiency of the proposed method.