On the convergence rate of Douglas-Rachford operator splitting method

• 成果类型: Article
• 署名作者: He, Bingsheng; Yuan, Xiaoming
• 署名单位: Nanjing University; Hong Kong Baptist University
• 刊物名称: MATHEMATICAL PROGRAMMING
• ISSN/ISSBN: 0025-5610
• DOI: 10.1007/s10107-014-0805-x
• 发表日期: 2015
• 页码: 715-722
• 关键词: Monotone; projection; algorithm

摘要

This note provides a simple proof of a worst-case convergence rate measured by the iteration complexity for the Douglas-Rachford operator splitting method for finding a root of the sum of two maximal monotone set-valued operators. The accuracy of an iterate to the solution set is measured by the residual of a characterization of the original problem, which is different from conventional measures such as the distance to the solution set.