| On a New Analysis Framework for the Linear Convergence of Relaxed Operator Splitting Methods |
| Received:March 20, 2021 Revised:October 16, 2021 |
| Key Words:
averaged operator negatively averaged operator relaxed forward-backward splitting method proximal point algorithm
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| Fund Project:Supported by the National Natural Science Foundation of China (Grant Nos.11801455; 11871059; 11971238), China Postdoctoral Science Foundation (Grant Nos.2019M663459; 2020T130081), the Applied Basic Project of Sichuan Province (Grant No.2020YJ0111) and the Open Project of Key Laboratory of School of Mathematical Sciences, Chongqing Normal University (Grant No.CSSXKFKTM202004). |
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| Abstract: |
| In this paper, we propose a new analysis framework to study the linear convergence of relaxed operator splitting methods, which can be viewed as an extension of the classic Krasnosel'ski$\breve{\mbox{i}}$-Mann iteration and Banach-Picard contraction. As applications, we derive the linear convergence of the generalized proximal point algorithm and the relaxed forward-backward splitting method in a simple and elegant way. |
| Citation: |
| DOI:10.3770/j.issn:2095-2651.2022.02.010 |
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