Inertial Douglas-Rachford splitting for monotone inclusion problems
Inertial Douglas-Rachford splitting for monotone inclusion problems
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DOI：
10.1016/j.amc.2015.01.017
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发表时间：
2015-04-01
影响因子：
4
通讯作者：
Hendrich, Christopher
中科院分区：
文献类型：
--
作者：
Bot, Radu Ioan;Csetnek, Ernoe Robert;Hendrich, Christopher
本文提出了一个求解Hilbert空间中两个极大单调算子和的零点集的惯性Douglas-Rachford分裂算法，并研究了它的收敛性。为此，我们制定的第一个惯性版本的Krasnosel'skiii-Mann算法近似的非扩张算子的不动点集，为此，我们还提供了一个详尽的收敛性分析。通过使用产品空间的方法，我们采用这些结果解决单调包含问题，涉及线性组成和平行和型运营商，并以这种方式提供迭代计划，其中每个最大单调映射分别访问通过其预解式。我们还考虑了求解原始-对偶非光滑凸优化问题的特殊情况，并通过聚类和位置理论中的一些数值实验来说明理论结果。(C)2015 Elsevier Inc. All rights reserved.
We propose an inertial Douglas-Rachford splitting algorithm for finding the set of zeros of the sum of two maximally monotone operators in Hilbert spaces and investigate its convergence properties. To this end we formulate first the inertial version of the Krasnosel'skii-Mann algorithm for approximating the set of fixed points of a nonexpansive operator, for which we also provide an exhaustive convergence analysis. By using a product space approach we employ these results to the solving of monotone inclusion problems involving linearly composed and parallel-sum type operators and provide in this way iterative schemes where each of the maximally monotone mappings is accessed separately via its resolvent. We consider also the special instance of solving a primal-dual pair of nonsmooth convex optimization problems and illustrate the theoretical results via some numerical experiments in clustering and location theory. (C) 2015 Elsevier Inc. All rights reserved.