KMS Of Academy of mathematics and systems sciences, CAS
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 | |
发表期刊 | JOURNAL OF GLOBAL OPTIMIZATION |
ISSN | 0925-5001 |
卷号 | 73期号:4页码:801-824 |
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. |
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 |
DOI | 10.1007/s10898-018-0727-x |
语种 | 英语 |
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 |
WOS类目 | Operations Research & Management Science ; Mathematics, Applied |
WOS记录号 | WOS:000462013800006 |
出版者 | SPRINGER |
引用统计 | |
文献类型 | 期刊论文 |
条目标识符 | http://ir.amss.ac.cn/handle/2S8OKBNM/34256 |
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.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 |
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. |
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