Randomized subspace correction methods for convex optimization
Fuente:
arXiv
Salvato in:
| Autori principali: | , , |
|---|---|
| Natura: | Preprint |
| Pubblicazione: |
2025
|
| Soggetti: | |
| Accesso online: | |
| Tags: |
Aggiungi Tag
Nessun Tag, puoi essere il primo ad aggiungerne!!
|
| _version_ | 1866911622106185728 |
|---|---|
| author | Jiang, Boou Park, Jongho Xu, Jinchao |
| author_facet | Jiang, Boou Park, Jongho Xu, Jinchao |
| contents | This paper introduces an abstract framework for randomized subspace correction methods for convex optimization, which unifies and generalizes a broad class of existing algorithms, including domain decomposition, multigrid, and block coordinate descent methods. We provide a convergence rate analysis ranging from minimal assumptions to more practical settings, such as sharpness and strong convexity. While most existing studies on block coordinate descent methods focus on nonoverlapping decompositions and smooth or strongly convex problems, our framework extends to more general settings involving arbitrary space decompositions, inexact local solvers, and problems with weaker smoothness or convexity assumptions. The proposed framework is broadly applicable to convex optimization problems arising in areas such as nonlinear partial differential equations, imaging, and data science. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2507_01415 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Randomized subspace correction methods for convex optimization Jiang, Boou Park, Jongho Xu, Jinchao Optimization and Control Numerical Analysis 90C25, 65N55, 65J05, 90C06 This paper introduces an abstract framework for randomized subspace correction methods for convex optimization, which unifies and generalizes a broad class of existing algorithms, including domain decomposition, multigrid, and block coordinate descent methods. We provide a convergence rate analysis ranging from minimal assumptions to more practical settings, such as sharpness and strong convexity. While most existing studies on block coordinate descent methods focus on nonoverlapping decompositions and smooth or strongly convex problems, our framework extends to more general settings involving arbitrary space decompositions, inexact local solvers, and problems with weaker smoothness or convexity assumptions. The proposed framework is broadly applicable to convex optimization problems arising in areas such as nonlinear partial differential equations, imaging, and data science. |
| title | Randomized subspace correction methods for convex optimization |
| topic | Optimization and Control Numerical Analysis 90C25, 65N55, 65J05, 90C06 |
| url | https://arxiv.org/abs/2507.01415 |