On the O ( 1 / t ) $O(1/t)$ convergence rate of the alternating direction method with LQP regularization for solving structured variational inequality problems

In this paper, we propose a parallel descent LQP alternating direction method for solving structured variational inequality with three separable operators. The $O(1/t)$ convergence rate for this method is studied. We also present some numerical examples to illustrate the efficiency of the proposed method. The results presented in this paper extend and improve some well-known results in the literature.