A reflected forward-backward splitting algorithmic framework
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arXiv
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| Main Authors: | , , , |
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| Format: | Preprint |
| Published: |
2026
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| Subjects: | |
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| _version_ | 1866916021292498944 |
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| author | Zheng, Haowen Fu, Yongyu Dong, Qiao-Li Li, Shuangbao |
| author_facet | Zheng, Haowen Fu, Yongyu Dong, Qiao-Li Li, Shuangbao |
| contents | In this paper, we propose a reflected forward-backward splitting algorithic framework for finding a zero of the sum of finitely many monotone op-erators, including maximally monotone operators, cocoercive operators, and monotone and Lipschitz continuous operators. We provide a unified convergence analysis under mild conditions, eliminating the need to analyze the convergence of each algorithm individually. The heuristic strategies for matrix selections are proposed through a numerical experiment, based on which a new algorithm is derived. A further numerical experiment on the regularized saddle-point problem is then presented to demonstrate the effectiveness of the proposed algorithm. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2605_17731 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | A reflected forward-backward splitting algorithmic framework Zheng, Haowen Fu, Yongyu Dong, Qiao-Li Li, Shuangbao Optimization and Control In this paper, we propose a reflected forward-backward splitting algorithic framework for finding a zero of the sum of finitely many monotone op-erators, including maximally monotone operators, cocoercive operators, and monotone and Lipschitz continuous operators. We provide a unified convergence analysis under mild conditions, eliminating the need to analyze the convergence of each algorithm individually. The heuristic strategies for matrix selections are proposed through a numerical experiment, based on which a new algorithm is derived. A further numerical experiment on the regularized saddle-point problem is then presented to demonstrate the effectiveness of the proposed algorithm. |
| title | A reflected forward-backward splitting algorithmic framework |
| topic | Optimization and Control |
| url | https://arxiv.org/abs/2605.17731 |