A modified forward-backward splitting method for maximal monotone mappings
A modified forward-backward splitting method for maximal monotone mappings
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DOI：
10.1137/s0363012998338806
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发表时间：
2000-02-02
影响因子：
2.2
通讯作者：
Tseng, P
中科院分区：
文献类型：
--
作者：
Tseng, P
本文研究了求两个极大单调映象之和的零点的前后向分裂方法。当正向映射的逆是强单调的时，这种方法是收敛的。我们提出了一个修改，这种方法的精神，单调变分不等式的超梯度方法，该方法收敛，假设只有向前映射是（Lipschitz）连续的一些封闭的凸子集的域。该修改需要在每次迭代时附加向前步骤和投影步骤。讨论了该方法在凸规划分解和单调变分不等式分解中的应用。
We consider the forward-backward splitting method for finding a zero of the sum of two maximal monotone mappings. This method is known to converge when the inverse of the forward mapping is strongly monotone. We propose a modification to this method, in the spirit of the extragradient method for monotone variational inequalities, under which the method converges assuming only the forward mapping is (Lipschitz) continuous on some closed convex subset of its domain. The modification entails an additional forward step and a projection step at each iteration. Applications of the modified method to decomposition in convex programming and monotone variational inequalities are discussed.