Deep Centralization for the Circumcentered Reflection Method
Fuente:
arXiv
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| Autore principale: | |
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| Natura: | Preprint |
| Pubblicazione: |
2025
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| _version_ | 1866911303856029696 |
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| author | Barros, Pablo |
| author_facet | Barros, Pablo |
| contents | We introduce the extended centralized circumcentered reflection method (ecCRM), a framework for two-set convex feasibility that encompasses the classical centralized CRM (cCRM) of Behling, Bello-Cruz, Iusem and Santos as a special case. Our method replaces the fixed centralization step of cCRM with an admissible operator $T$ and a parameter $α$, allowing control over computational cost and step quality. We show that ecCRM retains global convergence, linear rates under mild regularity, and superlinearity for smooth manifolds. Numerical experiments on large-scale matrix completion indicate that deeper operators can dramatically reduce overall runtime, and tests on high-dimensional ellipsoids show that vanishing step sizes can yield significant acceleration, validating the practical utility of both algorithmic components of ecCRM. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2512_05324 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Deep Centralization for the Circumcentered Reflection Method Barros, Pablo Optimization and Control 65K05, 65B99, 90C25 We introduce the extended centralized circumcentered reflection method (ecCRM), a framework for two-set convex feasibility that encompasses the classical centralized CRM (cCRM) of Behling, Bello-Cruz, Iusem and Santos as a special case. Our method replaces the fixed centralization step of cCRM with an admissible operator $T$ and a parameter $α$, allowing control over computational cost and step quality. We show that ecCRM retains global convergence, linear rates under mild regularity, and superlinearity for smooth manifolds. Numerical experiments on large-scale matrix completion indicate that deeper operators can dramatically reduce overall runtime, and tests on high-dimensional ellipsoids show that vanishing step sizes can yield significant acceleration, validating the practical utility of both algorithmic components of ecCRM. |
| title | Deep Centralization for the Circumcentered Reflection Method |
| topic | Optimization and Control 65K05, 65B99, 90C25 |
| url | https://arxiv.org/abs/2512.05324 |