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

doi:10.1007/s10898-018-0727-x

	MiKM: multi-step inertial Krasnosel'skii-Mann algorithm and its applications
	Dong, Q. L.7,8; Huang, J. Z.5,6; Li, X. H.7,8; Cho, Y. J.2,3,4; Rassias, Th. M.1
刊名	JOURNAL OF GLOBAL OPTIMIZATION
	2019-04-01
卷号	73 期号:4 页码:801-824
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
ISSN号	0925-5001
DOI	10.1007/s10898-018-0727-x
英文摘要	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.
资助项目	National Natural Science Foundation of China[71602144] ; Open Fund of Tianjin Key Lab for Advanced Signal Processing[2016ASP-TJ01]
WOS研究方向	Operations Research & Management Science ; Mathematics
语种	英语
出版者	SPRINGER
WOS记录号	WOS:000462013800006
内容类型	期刊论文
源URL	[http://ir.amss.ac.cn/handle/2S8OKBNM/34255]
专题	中国科学院数学与系统科学研究院
通讯作者	Dong, Q. L.
作者单位	1.Natl Tech Univ Athens, Dept Math, Zografou Campus, Athens 15780, Greece 2.Univ Elect Sci & Technol China, Sch Math Sci, Chengdu 611731, Sichuan, Peoples R China 3.Gyeongsang Natl Univ, RINS, Jinju 660701, South Korea 4.Gyeongsang Natl Univ, Dept Math Educ, Jinju 660701, South Korea 5.Univ Chinese Acad Sci, Sch Math Sci, Beijing 100049, Peoples R China 6.Chinese Acad Sci, Acad Math & Syst Sci, Inst Computat Math & Sci Engn Comp, LSEC, Beijing 100190, Peoples R China 7.Civil Aviat Univ China, Coll Sci, Tianjin 300300, Peoples R China 8.Civil Aviat Univ China, Tianjin Key Lab Adv Signal Proc, Tianjin 300300, Peoples R China
推荐引用方式 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.