Weak and Strong Convergence of Split Douglas-Rachford Algorithms for Monotone Inclusions

被引：0
|
作者：
Lv, Tianqi [1 ]
Xu, Hong-Kun [1 ]
机构：
[1] Hangzhou Dianzi Univ, Dept Math, Sch Sci, Hangzhou 310018, Peoples R China
来源：
CARPATHIAN JOURNAL OF MATHEMATICS | 2024年 / 40卷 / 03期
基金：
澳大利亚研究理事会; 中国国家自然科学基金;
关键词：
Monotone inclusion; nonexpansive mapping; fixed-point; primal-dual splitting; split Douglas-Rachford; nonstandard metric; projection; FIXED-POINTS;
D O I：
10.37193/CJM.2024.03.17
中图分类号：
O29 [应用数学];
学科分类号：
070104 ;
摘要：
We are concerned in this paper with the convergence analysis of the primal-dual splitting (PDS) and the split Douglas-Rachford (SDR) algorithms for monotone inclusions by using an operator-oriented approach. We shall show that both PDS and SDR algorithms can be driven by a (firmly) nonexpansive mapping in a product Hilbert space. We are then able to apply the Krasnoselskii-Mann and Halpern fixed point algorithms to PDS and SDR to get weakly and strongly convergent algorithms for finding solutions of the primal and dual monotone inclusions. Moreover, an additional projection technique is used to derive strong convergence of a modified SDR algorithm.
引用
收藏
页码：805 / 817
页数：13
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