A Modified Forward-backward Splitting Method for Maximal Monotone Mappings 1
A Modified Forward-backward Splitting Method for Maximal Monotone Mappings 1
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发表时间：
1998
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通讯作者：
P. Tseng
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作者：
P. Tseng
本文研究了确定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个方法，在精神上的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单调和（Lipschitz）连续的一些封闭的凸子集的域。修改需要在每次迭代中附加向前步骤和投影步骤。讨论了改进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 nding 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 modiication 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 monotone and (Lipschitz) continuous on some closed convex subset of its domain. The modiication entails an additional forward step and a projection step at each iteration. Applications of the modiied method to decomposition in convex programming and monotone variational inequalities are discussed.