解线性变分不等式问题的一个简单交替方向法

解变分不等式的交替方向法每一步需要解一个(几个)变分不等式子问题,算法的有效性受这些子问题的影响很大.本文提出了一个解线性变分不等式的简单的交替方向法. 在每一步迭代中,只需要做矩阵-向量乘法和到简单集合的投影,使得算法的效率得到保证.在适当的条件下证明了算法的全局收敛性.初步的数值结果表明,我们的新算法较原有同类算法有所改进.

A Simple Alternating Direction Method for Linear Variational Inequality Problems

The alternating direction methods for solving variational inequality problems needs to salve several subproblems, which are also variational inequalities. Thus, the efficiency of this type of methods is influenced by the methods for salving the subproblems. In this paper, we propose a simple alternating direction method. It needs only to perform some matrix - vector productions and projection onto a simple set. Under mild assumption, we show the global convergence of the method. Some preliminary computational results are reported, showing the efficiency of the proposed method.