| 松弛算子分裂法线性收敛性分析的新框架 |
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| 引用本文： | 李青菁,郭科. 松弛算子分裂法线性收敛性分析的新框架[J]. 数学研究及应用, 2022, 42(2): 199-205 |
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| 作者姓名： | 李青菁 郭科 |
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| 作者单位： | 西华师范大学数学与信息学院, 四川 南充 637002 |
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| 基金项目： | 国家自然科学基金(Grant Nos.11801455; 11871059; 11971238),中国博士后科学基金(Grant Nos.2019M663459; 2020T130081),四川省应用基础项目(Grant No.2020YJ0111),重庆师范大学数学科学学院教育部重点实验室开放项目(Grant No.CSSXKFKTM202004). |
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| 摘 要： | 提出了一种新的分析框架来研究松弛算子分裂法的线性收敛性,可以将这种框架看成是经典的Krasnosel''-Mann迭代和Banach-Picard收缩的扩展形式.随后,将提出的这个框架应用于分析广义邻近点算法和松弛向前向后分裂算法的线性收敛性,其过程十分简洁和直接.
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| 关 键 词： | 均值算子 负均值算子 松弛向前向后分裂算法 邻近点算法 |
| 收稿时间： | 2021-03-20 |
| 修稿时间： | 2021-10-16 |
On a New Analysis Framework for the Linear Convergence of Relaxed Operator Splitting Methods |
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| Qingjing LI,Ke GUO. On a New Analysis Framework for the Linear Convergence of Relaxed Operator Splitting Methods[J]. Journal of Mathematical Research with Applications, 2022, 42(2): 199-205 |
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| Authors: | Qingjing LI Ke GUO |
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| Affiliation: | School of Mathematics and Information, China West Normal University, Sichuan 637002, P. R. China |
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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. |
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| Keywords: | averaged operator negatively averaged operator relaxed forward-backward splitting method proximal point algorithm |
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