Fast Krasnoselskii-Mann Method with Overrelaxation and Preconditioners
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arXiv
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| Autori principali: | , , |
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| Natura: | Preprint |
| Pubblicazione: |
2024
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| _version_ | 1866911180103090176 |
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| author | Boţ, Radu I. Chenchene, Enis Fadili, Jalal M. |
| author_facet | Boţ, Radu I. Chenchene, Enis Fadili, Jalal M. |
| contents | We study accelerated Krasnoselskii-Mann-type methods with preconditioners in both continuous and discrete time. From a continuous-time model, we derive a generalized fast Krasnoselskii-Mann method, providing a new yet simple proof of convergence that leads to unprecedented flexibility in parameter tuning, allowing up to twice larger relaxation parameters. Our analysis unifies inertial and anchoring acceleration mechanisms and offers a broad range of parameter choices, which prove beneficial in practice. Additionally, we extend our analysis to the case where preconditioners are allowed to be degenerate, unifying the treatment of various splitting methods and establishing the weak convergence of shadow sequences. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2411_18574 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Fast Krasnoselskii-Mann Method with Overrelaxation and Preconditioners Boţ, Radu I. Chenchene, Enis Fadili, Jalal M. Optimization and Control Numerical Analysis 47J26, 47H04, 47H05, 65B99, 65K10, 90C25 We study accelerated Krasnoselskii-Mann-type methods with preconditioners in both continuous and discrete time. From a continuous-time model, we derive a generalized fast Krasnoselskii-Mann method, providing a new yet simple proof of convergence that leads to unprecedented flexibility in parameter tuning, allowing up to twice larger relaxation parameters. Our analysis unifies inertial and anchoring acceleration mechanisms and offers a broad range of parameter choices, which prove beneficial in practice. Additionally, we extend our analysis to the case where preconditioners are allowed to be degenerate, unifying the treatment of various splitting methods and establishing the weak convergence of shadow sequences. |
| title | Fast Krasnoselskii-Mann Method with Overrelaxation and Preconditioners |
| topic | Optimization and Control Numerical Analysis 47J26, 47H04, 47H05, 65B99, 65K10, 90C25 |
| url | https://arxiv.org/abs/2411.18574 |