Strong convergence of viscosity forward-backward algorithm to the sum of two accretive operators in Banach space

被引：3

作者：

Wang, Yamin ^{[1
,2
]}

Wang, Fenghui ^{[3
]}

Zhang, Haixia ^{[1
,2
]}

机构：

[1] Henan Normal Univ, Coll Math & Informat Sci, Xinxiang, Henan, Peoples R China

[2] Henan Normal Univ, Coll Math & Informat Sci, Henan Engn Lab Big Data Stat Anal & Optimal Contr, Xinxiang, Henan, Peoples R China

[3] Luoyang Normal Univ, Dept Math, Luoyang, Peoples R China

来源：

OPTIMIZATION | 2021年 / 70卷 / 01期

基金：

中国国家自然科学基金;

关键词：

Forward-backward algorithm; accretive operator; Banach space; strong convergence; VARIATIONAL INCLUSION; HILBERT-SPACES; SUPERIORIZATION; THEOREMS; OPTIMIZATION;

D O I：

10.1080/02331934.2019.1705299

中图分类号：

C93 [管理学]; O22 [运筹学];

学科分类号：

070105 ; 12 ; 1201 ; 1202 ; 120202 ;

摘要：

In recent years, the Forward-Backward algorithm (FBA) received much attention due to its various applications in image recovery, signal processing, and machine learning. In this paper, we consider the FBA in the setting of Banach spaces that are uniformly convex and q-uniformly smooth. We introduce two viscosity FBA, and one of them with weakly contractive mapping, which generalizes many previous results on the viscosity approximation method with fixed contraction. Moreover, we establish their strong convergences under more general conditions.

引用

页码：169 / 190

页数：22

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