Splitting the Forward-Backward Algorithm: A Full Characterization
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arXiv
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| Hauptverfasser: | , , , |
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| Format: | Preprint |
| Veröffentlicht: |
2025
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| _version_ | 1866916691356680192 |
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| author | Åkerman, Anton Chenchene, Enis Giselsson, Pontus Naldi, Emanuele |
| author_facet | Åkerman, Anton Chenchene, Enis Giselsson, Pontus Naldi, Emanuele |
| contents | We study frugal splitting algorithms with minimal lifting for solving monotone inclusion problems involving sums of maximal monotone and cocoercive operators. Building on a foundational result by Ryu, we fully characterize all methods that use only individual resolvent evaluations, direct evaluations of cocoercive operators, and minimal memory resources while ensuring convergence via averaged fixed-point iterations. We show that all such methods are captured by a unified framework, which includes known schemes and enables new ones with promising features. Systematic numerical experiments lead us to propose three design heuristics to achieve excellent performances in practice, yielding significant gains over existing methods. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2504_10999 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Splitting the Forward-Backward Algorithm: A Full Characterization Åkerman, Anton Chenchene, Enis Giselsson, Pontus Naldi, Emanuele Optimization and Control 47N10, 47H05, 47H09, 65K10, 90C25 We study frugal splitting algorithms with minimal lifting for solving monotone inclusion problems involving sums of maximal monotone and cocoercive operators. Building on a foundational result by Ryu, we fully characterize all methods that use only individual resolvent evaluations, direct evaluations of cocoercive operators, and minimal memory resources while ensuring convergence via averaged fixed-point iterations. We show that all such methods are captured by a unified framework, which includes known schemes and enables new ones with promising features. Systematic numerical experiments lead us to propose three design heuristics to achieve excellent performances in practice, yielding significant gains over existing methods. |
| title | Splitting the Forward-Backward Algorithm: A Full Characterization |
| topic | Optimization and Control 47N10, 47H05, 47H09, 65K10, 90C25 |
| url | https://arxiv.org/abs/2504.10999 |