SQP alternating direction method for structured variational inequalities

By combining the alternating direction method with square quadratic proximal (SQP) term, we propose an alternating direction method for solving linearly constrained separable convex programming with three separable operators. Each iteration of the proposed method contains a prediction and a correction, the predictor is obtained by solving SQP system and new iterate is obtained by a convex combination of the previous point and the one generated by a projection-type method along a descent direction. Global convergence of the new method is studied under certain assumptions. We also present some numerical results to illustrate the efficiency of the proposed method. The results presented in this paper extend and improve some well-known results in the literature.