Forward–Reflected–Backward Splitting Algorithms with Momentum: Weak, Linear and Strong Convergence Results
This paper studies the forward–reflected–backward splitting algorithm with momentum terms for monotone inclusion problem of the sum of a maximal monotone and Lipschitz continuous monotone operators in Hilbert spaces. The forward–reflected–backward splitting algorithm is an interesting algorithm for...
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| Vydáno v: | Journal of optimization theory and applications Ročník 201; číslo 3; s. 1364 - 1397 |
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| Jazyk: | angličtina |
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01.06.2024
Springer Nature B.V |
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| ISSN: | 0022-3239, 1573-2878 |
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| Abstract | This paper studies the forward–reflected–backward splitting algorithm with momentum terms for monotone inclusion problem of the sum of a maximal monotone and Lipschitz continuous monotone operators in Hilbert spaces. The forward–reflected–backward splitting algorithm is an interesting algorithm for inclusion problems with the sum of maximal monotone and Lipschitz continuous monotone operators due to the inherent feature of one forward evaluation and one backward evaluation per iteration it possesses. The results in this paper further explore the convergence behavior of the forward–reflected–backward splitting algorithm with momentum terms. We obtain weak, linear, and strong convergence results under the same inherent feature of one forward evaluation and one backward evaluation at each iteration. Numerical results show that forward–reflected–backward splitting algorithms with momentum terms are efficient and promising over some related splitting algorithms in the literature. |
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| AbstractList | This paper studies the forward–reflected–backward splitting algorithm with momentum terms for monotone inclusion problem of the sum of a maximal monotone and Lipschitz continuous monotone operators in Hilbert spaces. The forward–reflected–backward splitting algorithm is an interesting algorithm for inclusion problems with the sum of maximal monotone and Lipschitz continuous monotone operators due to the inherent feature of one forward evaluation and one backward evaluation per iteration it possesses. The results in this paper further explore the convergence behavior of the forward–reflected–backward splitting algorithm with momentum terms. We obtain weak, linear, and strong convergence results under the same inherent feature of one forward evaluation and one backward evaluation at each iteration. Numerical results show that forward–reflected–backward splitting algorithms with momentum terms are efficient and promising over some related splitting algorithms in the literature. |
| Author | Adamu, Abubakar Yao, Yonghong Shehu, Yekini |
| Author_xml | – sequence: 1 givenname: Yonghong surname: Yao fullname: Yao, Yonghong organization: School of Mathematical Sciences, Tiangong University, Center for Advanced Information Technology, Kyung Hee University – sequence: 2 givenname: Abubakar surname: Adamu fullname: Adamu, Abubakar organization: Operational Research Center in Healthcare, Near East University, Charles Chidume Mathematics Institute, African University of Science and Technology – sequence: 3 givenname: Yekini surname: Shehu fullname: Shehu, Yekini email: yekini.shehu@zjnu.edu.cn organization: School of Mathematical Sciences, Zhejiang Normal University |
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| CitedBy_id | crossref_primary_10_1007_s40314_024_02876_3 crossref_primary_10_1016_j_matcom_2025_07_041 crossref_primary_10_1016_j_neucom_2024_128285 crossref_primary_10_1007_s12215_025_01212_w crossref_primary_10_1080_02331934_2025_2533490 |
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| SubjectTerms | Algorithms Applications of Mathematics Calculus of Variations and Optimal Control; Optimization Convergence Engineering Hilbert space Mathematics Mathematics and Statistics Momentum Operations Research/Decision Theory Operators (mathematics) Optimization Splitting Theory of Computation |
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| Title | Forward–Reflected–Backward Splitting Algorithms with Momentum: Weak, Linear and Strong Convergence Results |
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