A Three-Operator Splitting Scheme Derived from Three-Block ADMM
Fuente:
arXiv
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| Autori principali: | , , , |
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| Natura: | Preprint |
| Pubblicazione: |
2024
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| _version_ | 1866918152670019584 |
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| author | Anshika, Anshika Li, Jiaxing Ghosh, Debdas Zhang, Xiangxiong |
| author_facet | Anshika, Anshika Li, Jiaxing Ghosh, Debdas Zhang, Xiangxiong |
| contents | This work presents a new three-operator splitting method to handle monotone inclusion and convex optimization problems. The proposed splitting serves as another natural extension of the Douglas-Rachford splitting technique to problems involving three operators. For solving a composite convex minimization of a sum of three functions, its formula resembles but is different from Davis-Yin splitting and the dual formulation of the classical three-block ADMM. Numerical tests suggest that such a splitting scheme is robust in the sense of allowing larger step sizes. When two functions have orthogonal domains, the splitting operator can be proven 1/2-averaged, which implies convergence of the iteration scheme using any positive step size. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2411_00166 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | A Three-Operator Splitting Scheme Derived from Three-Block ADMM Anshika, Anshika Li, Jiaxing Ghosh, Debdas Zhang, Xiangxiong Optimization and Control 47H05, 65K05, 65K15, 90C25 This work presents a new three-operator splitting method to handle monotone inclusion and convex optimization problems. The proposed splitting serves as another natural extension of the Douglas-Rachford splitting technique to problems involving three operators. For solving a composite convex minimization of a sum of three functions, its formula resembles but is different from Davis-Yin splitting and the dual formulation of the classical three-block ADMM. Numerical tests suggest that such a splitting scheme is robust in the sense of allowing larger step sizes. When two functions have orthogonal domains, the splitting operator can be proven 1/2-averaged, which implies convergence of the iteration scheme using any positive step size. |
| title | A Three-Operator Splitting Scheme Derived from Three-Block ADMM |
| topic | Optimization and Control 47H05, 65K05, 65K15, 90C25 |
| url | https://arxiv.org/abs/2411.00166 |