MiKM: multi-step inertial Krasnosel'skii-Mann algorithm and its applications

被引：62

作者：

Dong, Q. L. ^{[1
,2
]}

Huang, J. Z. ^{[3
,4
]}

Li, X. H. ^{[1
,2
]}

Cho, Y. J. ^{[5
,6
,7
]}

Rassias, Th. M. ^{[8
]}

机构：

[1] Civil Aviat Univ China, Tianjin Key Lab Adv Signal Proc, Tianjin 300300, Peoples R China

[2] Civil Aviat Univ China, Coll Sci, Tianjin 300300, Peoples R China

[3] Chinese Acad Sci, Acad Math & Syst Sci, Inst Computat Math & Sci Engn Comp, LSEC, Beijing 100190, Peoples R China

[4] Univ Chinese Acad Sci, Sch Math Sci, Beijing 100049, Peoples R China

[5] Gyeongsang Natl Univ, Dept Math Educ, Jinju 660701, South Korea

[6] Gyeongsang Natl Univ, RINS, Jinju 660701, South Korea

[7] Univ Elect Sci & Technol China, Sch Math Sci, Chengdu 611731, Sichuan, Peoples R China

[8] Natl Tech Univ Athens, Dept Math, Zografou Campus, Athens 15780, Greece

来源：

JOURNAL OF GLOBAL OPTIMIZATION | 2019年 / 73卷 / 04期

基金：

中国国家自然科学基金;

关键词：

Nonexpansive operator; Multi-step inertial Krasnosel'skii-Mann algorithm; Monotone inclusion; Bounded perturbation resilience; Douglas-Rachford splitting method; Forward-backward splitting method; Backward-forward splitting method; Davis-Yin splitting method; GRADIENT METHODS; SUPERIORIZATION;

D O I：

10.1007/s10898-018-0727-x

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 this paper, we first introduce a multi-step inertial Krasnosel'skii-Mann algorithm (MiKM) for nonexpansive operators in real Hilbert spaces. We give the convergence of the MiKM by investigating the convergence of the Krasnosel'skii-Mann algorithm with perturbations. We also establish global pointwise and ergodic iteration complexity bounds of the Krasnosel'skii-Mann algorithm with perturbations. Based on the MiKM, we construct some multi-step inertial splitting methods, including the multi-step inertial Douglas-Rachford splitting method (MiDRS), the multi-step inertial forward-backward splitting method, multi-step inertial backward-forward splitting method and and the multi-step inertial Davis-Yin splitting method. Numerical experiments are provided to illustrate the advantage of the MiDRS over the one-step inertial DRS and the original DRS.

引用

页码：801 / 824

页数：24

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