Convergence Analyses of Davis-Yin Splitting via Scaled Relative Graphs
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arXiv
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| Hauptverfasser: | , , |
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| Format: | Preprint |
| Veröffentlicht: |
2022
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| _version_ | 1866910415917678592 |
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| author | Lee, Jongmin Yi, Soheun Ryu, Ernest K. |
| author_facet | Lee, Jongmin Yi, Soheun Ryu, Ernest K. |
| contents | Davis-Yin splitting (DYS) has found a wide range of applications in optimization, but its linear rates of convergence have not been studied extensively. The scaled relative graph (SRG) simplifies the convergence analysis of operator splitting methods by mapping the action of the operator onto the complex plane, but the prior SRG theory did not fully apply to the DYS operator. In this work, we formalize an SRG theory for the DYS operator and use it to obtain tighter contraction factors. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2207_04015 |
| institution | arXiv |
| publishDate | 2022 |
| record_format | arxiv |
| spellingShingle | Convergence Analyses of Davis-Yin Splitting via Scaled Relative Graphs Lee, Jongmin Yi, Soheun Ryu, Ernest K. Optimization and Control Davis-Yin splitting (DYS) has found a wide range of applications in optimization, but its linear rates of convergence have not been studied extensively. The scaled relative graph (SRG) simplifies the convergence analysis of operator splitting methods by mapping the action of the operator onto the complex plane, but the prior SRG theory did not fully apply to the DYS operator. In this work, we formalize an SRG theory for the DYS operator and use it to obtain tighter contraction factors. |
| title | Convergence Analyses of Davis-Yin Splitting via Scaled Relative Graphs |
| topic | Optimization and Control |
| url | https://arxiv.org/abs/2207.04015 |