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MiKM: multi-step inertial Krasnosel'skii-Mann algorithm and its applications
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
2019-04-01
Source PublicationJOURNAL OF GLOBAL OPTIMIZATION
ISSN0925-5001
Volume73Issue:4Pages:801-824
AbstractIn 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.
KeywordNonexpansive 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
DOI10.1007/s10898-018-0727-x
Language英语
Funding ProjectNational Natural Science Foundation of China[71602144] ; Open Fund of Tianjin Key Lab for Advanced Signal Processing[2016ASP-TJ01]
WOS Research AreaOperations Research & Management Science ; Mathematics
WOS SubjectOperations Research & Management Science ; Mathematics, Applied
WOS IDWOS:000462013800006
PublisherSPRINGER
Citation statistics
Cited Times:1[WOS]   [WOS Record]     [Related Records in WOS]
Document Type期刊论文
Identifierhttp://ir.amss.ac.cn/handle/2S8OKBNM/34256
Collection中国科学院数学与系统科学研究院
Affiliation1.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
Recommended Citation
GB/T 7714
Dong, Q. L.,Huang, J. Z.,Li, X. H.,et al. MiKM: multi-step inertial Krasnosel'skii-Mann algorithm and its applications[J]. JOURNAL OF GLOBAL OPTIMIZATION,2019,73(4):801-824.
APA Dong, Q. L.,Huang, J. Z.,Li, X. H.,Cho, Y. J.,&Rassias, Th. M..(2019).MiKM: multi-step inertial Krasnosel'skii-Mann algorithm and its applications.JOURNAL OF GLOBAL OPTIMIZATION,73(4),801-824.
MLA Dong, Q. L.,et al."MiKM: multi-step inertial Krasnosel'skii-Mann algorithm and its applications".JOURNAL OF GLOBAL OPTIMIZATION 73.4(2019):801-824.
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