A DOUGLAS-RACHFORD TYPE PRIMAL-DUAL METHOD FOR SOLVING INCLUSIONS WITH MIXTURES OF COMPOSITE AND PARALLEL-SUM TYPE MONOTONE OPERATORS
A DOUGLAS-RACHFORD TYPE PRIMAL-DUAL METHOD FOR SOLVING INCLUSIONS WITH MIXTURES OF COMPOSITE AND PARALLEL-SUM TYPE MONOTONE OPERATORS
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DOI：
10.1137/120901106
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发表时间：
2013-01-01
影响因子：
3.1
通讯作者：
Hendrich, Christopher
中科院分区：
文献类型：
--
作者：
Bot, Radu Ioan;Hendrich, Christopher
在本文中，我们提出了两种不同的原始-对偶分裂算法求解包含的混合组合和平行和型单调算子依赖于一个不精确的Douglas-Rachford分裂方法，但适用于不同的基础Hilbert空间。最重要的是，该算法允许一个处理的有界线性算子和集值算子的单调包含问题的制定分别在每次迭代，后者被单独访问通过其resolvents。通过定位和图像去噪问题的一些数值实验，强调了原始-对偶算法的性能。
In this paper we propose two different primal-dual splitting algorithms for solving inclusions involving mixtures of composite and parallel-sum type monotone operators which rely on an inexact Douglas-Rachford splitting method, but applied in different underlying Hilbert spaces. Most importantly, the algorithms allow one to process the bounded linear operators and the set-valued operators occurring in the formulation of the monotone inclusion problem separately at each iteration, the latter being individually accessed via their resolvents. The performance of the primal-dual algorithms is emphasized via some numerical experiments on location and image denoising problems.