松弛算子分裂法线性收敛性分析的新框架

On a New Analysis Framework for the Linear Convergence of Relaxed Operator Splitting Methods

中文关键词:  均值算子  负均值算子  松弛向前向后分裂算法  邻近点算法

英文关键词:averaged operator  negatively averaged operator  relaxed forward-backward splitting method  proximal point algorithm

中文摘要:

      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.

英文摘要:

      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.