Convergence of an inertial reflected–forward–backward splitting algorithm for solving monotone inclusion problems with application to image recovery
We first propose a reflected–forward–backward splitting algorithm with two inertial effects for solving monotone inclusions and then establish that the sequence of iterates it generates converges weakly in a real Hilbert space to a zero of the sum of a set-valued maximal monotone operator and a sing...
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| Vydané v: | Journal of computational and applied mathematics Ročník 460; s. 116405 |
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| Jazyk: | English |
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Elsevier B.V
01.05.2025
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| ISSN: | 0377-0427 |
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| Abstract | We first propose a reflected–forward–backward splitting algorithm with two inertial effects for solving monotone inclusions and then establish that the sequence of iterates it generates converges weakly in a real Hilbert space to a zero of the sum of a set-valued maximal monotone operator and a single-valued monotone Lipschitz continuous operator. The proposed algorithm involves only one forward evaluation of the single-valued operator and one backward evaluation of the set-valued operator at each iteration. One inertial parameter is non-negative while the other is non-positive. These features are absent in many other available inertial splitting algorithms in the literature. Finally, we discuss some problems in image restoration in connection with the implementation of our algorithm and compare it with some known related algorithms in the literature. |
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| AbstractList | We first propose a reflected–forward–backward splitting algorithm with two inertial effects for solving monotone inclusions and then establish that the sequence of iterates it generates converges weakly in a real Hilbert space to a zero of the sum of a set-valued maximal monotone operator and a single-valued monotone Lipschitz continuous operator. The proposed algorithm involves only one forward evaluation of the single-valued operator and one backward evaluation of the set-valued operator at each iteration. One inertial parameter is non-negative while the other is non-positive. These features are absent in many other available inertial splitting algorithms in the literature. Finally, we discuss some problems in image restoration in connection with the implementation of our algorithm and compare it with some known related algorithms in the literature. |
| ArticleNumber | 116405 |
| Author | Izuchukwu, Chinedu Reich, Simeon Shehu, Yekini |
| Author_xml | – sequence: 1 givenname: Chinedu surname: Izuchukwu fullname: Izuchukwu, Chinedu email: chinedu.izuchukwu@wits.ac.za organization: School of Mathematics, University of the Witwatersrand, Private Bag 3, Johannesburg, 2050, South Africa – sequence: 2 givenname: Simeon surname: Reich fullname: Reich, Simeon email: sreich@technion.ac.il organization: Department of Mathematics, The Technion – Israel Institute of Technology, 32000 Haifa, Israel – sequence: 3 givenname: Yekini orcidid: 0000-0001-9224-7139 surname: Shehu fullname: Shehu, Yekini email: yekini.shehu@zjnu.edu.cn organization: School of Mathematical Sciences, Zhejiang Normal University, Jinhua 321004, People's Republic of China |
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| Cites_doi | 10.1137/S0363012998338806 10.1016/0022-247X(79)90234-8 10.1007/s00025-022-01694-5 10.1137/080716542 10.1007/s10851-014-0523-2 10.1023/A:1025499305742 10.1137/14097238X 10.1137/10081602X 10.1080/01630563.2013.763825 10.1007/s11590-015-0904-5 10.1007/s11784-018-0526-5 10.1016/j.cam.2023.115702 10.1137/17M112806X 10.1016/j.cnsns.2024.108110 10.1080/10556788.2017.1300899 10.1007/s11228-020-00542-4 10.1137/18M1207260 10.1007/s10898-018-0727-x 10.1016/S0377-0427(02)00906-8 10.1137/0716071 10.1016/0041-5553(64)90137-5 10.1007/s10915-023-02311-5 10.1002/mma.8578 10.1080/02331934.2021.1981895 |
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| Keywords | 47H10 Monotone inclusion 49J20 Image restoration problem 49J40 Optimal control 47H09 Inertial method Monotone operator Reflected–forward–backward algorithm |
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| SubjectTerms | Image restoration problem Inertial method Monotone inclusion Monotone operator Optimal control Reflected–forward–backward algorithm |
| Title | Convergence of an inertial reflected–forward–backward splitting algorithm for solving monotone inclusion problems with application to image recovery |
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