A MONOTONE plus SKEW SPLITTING MODEL FOR COMPOSITE MONOTONE INCLUSIONS IN DUALITY
A MONOTONE plus SKEW SPLITTING MODEL FOR COMPOSITE MONOTONE INCLUSIONS IN DUALITY
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DOI：
10.1137/10081602x
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发表时间：
2011-01-01
影响因子：
3.1
通讯作者：
Combettes, Patrick L.
中科院分区：
文献类型：
--
作者：
Briceno-Arias, Luis M.;Combettes, Patrick L.
本文的基本原理是：同时求解一大类复合单调包含及其对偶的问题可归结为求极大单调算子与线性斜伴算子之和的零点的问题。开发了一个算法框架，用于在Hilbert空间环境中解决这一一般问题。在此框架下，对含有复合单调算子的包含问题，给出了新的原-对偶分裂算法，并得到了收敛结果。这些算法的简单性和有效性来自于它们以完全分解的方式操作，在这种意义上，涉及的单调算子和线性变换在每次迭代时被单独激活。与现有方法进行了比较，并展示了其在复合变分问题中的应用。
The principle underlying this paper is the basic observation that the problem of simultaneously solving a large class of composite monotone inclusions and their duals can be reduced to that of finding a zero of the sum of a maximally monotone operator and a linear skew-adjoint operator. An algorithmic framework is developed for solving this generic problem in a Hilbert space setting. New primal-dual splitting algorithms are derived from this framework for inclusions involving composite monotone operators, and convergence results are established. These algorithms draw their simplicity and efficacy from the fact that they operate in a fully decomposed fashion in the sense that the monotone operators and the linear transformations involved are activated separately at each iteration. Comparisons with existing methods are made and applications to composite variational problems are demonstrated.