Extending Douglas-Rachford Splitting for Convex Optimization
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arXiv
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| Autori principali: | , , |
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| Natura: | Preprint |
| Pubblicazione: |
2025
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| _version_ | 1866915669048557568 |
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| author | Nilsson, Max Åkerman, Anton Giselsson, Pontus |
| author_facet | Nilsson, Max Åkerman, Anton Giselsson, Pontus |
| contents | The Douglas-Rachford splitting method is a classical and widely used algorithm for solving monotone inclusions involving the sum of two maximally monotone operators. It was recently shown to be the unique frugal, no-lifting resolvent-splitting method that is unconditionally convergent in the general two-operator setting. In this work, we show that this uniqueness does not hold in the convex optimization case: when the operators are subdifferentials of proper, closed, convex functions, a strictly larger class of frugal, no-lifting resolvent-splitting methods is unconditionally convergent. We provide a complete characterization of all such methods in the convex optimization setting and prove that this characterization is sharp: unconditional convergence holds exactly on the identified parameter regions. These results immediately yield new families of convergent ADMM-type and Chambolle-Pock-type methods obtained through their Douglas-Rachford reformulations. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2511_19637 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Extending Douglas-Rachford Splitting for Convex Optimization Nilsson, Max Åkerman, Anton Giselsson, Pontus Optimization and Control The Douglas-Rachford splitting method is a classical and widely used algorithm for solving monotone inclusions involving the sum of two maximally monotone operators. It was recently shown to be the unique frugal, no-lifting resolvent-splitting method that is unconditionally convergent in the general two-operator setting. In this work, we show that this uniqueness does not hold in the convex optimization case: when the operators are subdifferentials of proper, closed, convex functions, a strictly larger class of frugal, no-lifting resolvent-splitting methods is unconditionally convergent. We provide a complete characterization of all such methods in the convex optimization setting and prove that this characterization is sharp: unconditional convergence holds exactly on the identified parameter regions. These results immediately yield new families of convergent ADMM-type and Chambolle-Pock-type methods obtained through their Douglas-Rachford reformulations. |
| title | Extending Douglas-Rachford Splitting for Convex Optimization |
| topic | Optimization and Control |
| url | https://arxiv.org/abs/2511.19637 |