On a new analysis framework for the linear convergence of relaxed operator splitting methods
Received:March 20, 2021  Revised:August 10, 2021
Key Word: averaged operator,negatively averaged operator,relaxed forward-backward splitting method,proximal point algorithm  
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Ke Guo School of Mathematics and Information, China West Normal University 四川省南充市顺庆区师大路1号西华师范大学数学与信息学院
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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'skii-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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