求解结构型单调变分不等式的下降型LQP交替方向法

In this paper, we propose a new descend logarithmic-quadratic proximal (LQP) alternating direction method for solving monotone variational inequalities with a separable structure. The new method includes two steps: prediction step and correction step. The prediction point is generated by the iterative format of LQP alternating direction method. Using prediction point we construct a new descend direction. The correction point is obtained by a convex combination of the previous point and the one generated by a projection-type method along this descent direction. During the analysis of the algorithm, we present a way to select optimal step and under appropriate assumption we prove the global convergence of the algorithm. Finally, Some numerical results demonstrate that the new method is effective in practice．