Four-operator reflected forward-backward algorithm for solving monotone inclusions involving Lipschitzian operator
In this work, using a discretisation of continuous-time dynamical systems, we design a novel splitting algorithm without the lifting technique for finding the sum of three maximal monotone operators and a monotone operator with Lipschitz continuity. In theory, we analyze the weak and strong converge...
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| Veröffentlicht in: | Communications in nonlinear science & numerical simulation Jg. 153; S. 109485 |
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| Abstract | In this work, using a discretisation of continuous-time dynamical systems, we design a novel splitting algorithm without the lifting technique for finding the sum of three maximal monotone operators and a monotone operator with Lipschitz continuity. In theory, we analyze the weak and strong convergence of the proposed splitting algorithm and show the sublinear convergence rate. The practical efficacy of the proposed algorithm is validated through image restoration experiments, where it outperforms existing methods. |
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| AbstractList | In this work, using a discretisation of continuous-time dynamical systems, we design a novel splitting algorithm without the lifting technique for finding the sum of three maximal monotone operators and a monotone operator with Lipschitz continuity. In theory, we analyze the weak and strong convergence of the proposed splitting algorithm and show the sublinear convergence rate. The practical efficacy of the proposed algorithm is validated through image restoration experiments, where it outperforms existing methods. |
| ArticleNumber | 109485 |
| Author | Cao, Yu Ur Rehman, Habib Yao, Jen-Chih Wang, Yuanheng Shehu, Yekini |
| Author_xml | – sequence: 1 givenname: Yu surname: Cao fullname: Cao, Yu email: caoyu9504@126.com organization: School of Mathematical Sciences, China West Normal University, Nanchong,637009, PR China – sequence: 2 givenname: Yuanheng orcidid: 0000-0003-4079-2850 surname: Wang fullname: Wang, Yuanheng email: yhwang@zjnu.cn organization: School of Mathematical Sciences, Zhejiang Normal University, Jinhua,321004, China – sequence: 3 givenname: Habib surname: Ur Rehman fullname: Ur Rehman, Habib email: hrehman@zjnu.edu.cn organization: Center for General Education, China Medical University, Taichung, Taiwan – sequence: 4 givenname: Yekini surname: Shehu fullname: Shehu, Yekini email: yekini.shehu@zjnu.edu.cn organization: School of Mathematical Sciences, Zhejiang Normal University, Jinhua,321004, PR China – sequence: 5 givenname: Jen-Chih surname: Yao fullname: Yao, Jen-Chih email: yaojc@mail.cmu.edu.cn organization: Center for General Education, China Medical University Taichung, Taiwan and Academy of Romanian Scientists, Romania |
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| Cites_doi | 10.3390/sym10110563 10.1137/0314056 10.1007/s10851-014-0523-2 10.1137/S0363012998338806 10.1137/050626090 10.1137/18M1207260 10.1080/01630563.2013.763825 10.1007/s10957-013-0465-7 10.1007/s10589-022-00400-z 10.1007/s10107-019-01403-1 10.1007/s10957-016-0893-2 10.1080/02331934.2013.855210 10.1007/s10589-021-00291-6 10.1137/S1052623495290179 10.1007/s10915-021-01608-7 10.1137/090754297 10.1090/S0002-9947-1956-0084194-4 10.1007/s10957-019-01601-z 10.3390/math8050818 10.1016/0022-247X(79)90234-8 10.1137/10081602X 10.1080/02331934.2022.2098126 10.1080/10556788.2024.2307470 10.1215/S0012-7094-62-02933-2 10.1090/S0002-9904-1967-11761-0 10.1137/120872802 10.1137/0716071 10.1007/s11590-015-0904-5 10.1007/s10957-024-02501-7 10.1080/02331934.2024.2391004 10.1137/17M1120099 |
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| Keywords | 68Q25 Forward-backward splitting algorithm Maximal monotone 90C25 Lipschitz continuous 47H05 49M25 Reflected technique |
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| SubjectTerms | Forward-backward splitting algorithm Lipschitz continuous Maximal monotone Reflected technique |
| Title | Four-operator reflected forward-backward algorithm for solving monotone inclusions involving Lipschitzian operator |
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