An inexact alternating direction method for solving a class of structured variational inequalities
An inexact alternating direction method for solving a class of structured variational inequalities
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DOI：
10.1016/j.amc.2013.01.067
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发表时间：
2013-03
期刊：
影响因子：
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通讯作者：
A. Bnouhachem;H. Benazza;M. Khalfaoui
中科院分区：
文献类型：
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作者：
A. Bnouhachem;H. Benazza;M. Khalfaoui
交替方向法主要用于求解具有可分结构的大规模变分不等式问题。这种方法是有效的，因为它通过求解一系列容易得多的低维子问题来解决原始的高维变分不等式问题。在本文中，我们提出了一种不精确交替方向法。与二次近邻交替方向法相比，该方法求解的是一系列相关的非线性方程组，而不是一系列的子VIS。不精确的标准比他等人使用的标准要宽松得多。[7]。生成的序列关于解集是Fejér单调的，并且在适当的条件下证明了它的收敛。
The alternating direction method is mainly adopted to solve large-scale variational inequality problems with separable structure. The method is effective because it solves the original high-dimensional variational inequality problem by solving a series of much easier low-dimensional subproblems. In this paper, we present an inexact alternating directions method. Compared with the quadratic proximal alternating direction methods, the proposed method solves a series of related systems of nonlinear equations instead of a series of sub-VIs. The inexact criteria are more relaxed than the ones used by He et al. [7]. The generated sequence is Fejér monotone with respect to the solution set and the convergence is proved under suitable conditions.