Randomized subspace correction methods for convex optimization.
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| Title: | Randomized subspace correction methods for convex optimization. |
|---|---|
| Authors: | Jiang, Boou1 (AUTHOR) boou.jiang@kaust.edu.sa, Park, Jongho1 (AUTHOR) jongho.park@kaust.edu.sa, Xu, Jinchao1 (AUTHOR) jinchao.xu@kaust.edu.sa |
| Source: | Computers & Mathematics with Applications. Aug2026, Vol. 215, p135-154. 20p. |
| Subjects: | Domain decomposition methods, Multigrid methods (Numerical analysis), Algorithms, Convex programming, Imaging systems, Partial differential equations |
| Abstract: | 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. [ABSTRACT FROM AUTHOR] |
| Copyright of Computers & Mathematics with Applications is the property of Pergamon Press - An Imprint of Elsevier Science and its content may not be copied or emailed to multiple sites without the copyright holder's express written permission. Additionally, content may not be used with any artificial intelligence tools or machine learning technologies. However, users may print, download, or email articles for individual use. This abstract may be abridged. No warranty is given about the accuracy of the copy. Users should refer to the original published version of the material for the full abstract. (Copyright applies to all Abstracts.) | |
| Database: | Engineering Source |
| FullText | Text: Availability: 0 |
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| Header | DbId: egs DbLabel: Engineering Source An: 194227772 AccessLevel: 6 PubType: Academic Journal PubTypeId: academicJournal PreciseRelevancyScore: 0 |
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| Items | – Name: Title Label: Title Group: Ti Data: Randomized subspace correction methods for convex optimization. – Name: Author Label: Authors Group: Au Data: <searchLink fieldCode="AR" term="%22Jiang%2C+Boou%22">Jiang, Boou</searchLink><relatesTo>1</relatesTo> (AUTHOR)<i> boou.jiang@kaust.edu.sa</i><br /><searchLink fieldCode="AR" term="%22Park%2C+Jongho%22">Park, Jongho</searchLink><relatesTo>1</relatesTo> (AUTHOR)<i> jongho.park@kaust.edu.sa</i><br /><searchLink fieldCode="AR" term="%22Xu%2C+Jinchao%22">Xu, Jinchao</searchLink><relatesTo>1</relatesTo> (AUTHOR)<i> jinchao.xu@kaust.edu.sa</i> – Name: TitleSource Label: Source Group: Src Data: <searchLink fieldCode="JN" term="%22Computers+%26+Mathematics+with+Applications%22">Computers & Mathematics with Applications</searchLink>. Aug2026, Vol. 215, p135-154. 20p. – Name: Subject Label: Subjects Group: Su Data: <searchLink fieldCode="DE" term="%22Domain+decomposition+methods%22">Domain decomposition methods</searchLink><br /><searchLink fieldCode="DE" term="%22Multigrid+methods+%28Numerical+analysis%29%22">Multigrid methods (Numerical analysis)</searchLink><br /><searchLink fieldCode="DE" term="%22Algorithms%22">Algorithms</searchLink><br /><searchLink fieldCode="DE" term="%22Convex+programming%22">Convex programming</searchLink><br /><searchLink fieldCode="DE" term="%22Imaging+systems%22">Imaging systems</searchLink><br /><searchLink fieldCode="DE" term="%22Partial+differential+equations%22">Partial differential equations</searchLink> – Name: Abstract Label: Abstract Group: Ab Data: 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. [ABSTRACT FROM AUTHOR] – Name: AbstractSuppliedCopyright Label: Group: Ab Data: <i>Copyright of Computers & Mathematics with Applications is the property of Pergamon Press - An Imprint of Elsevier Science and its content may not be copied or emailed to multiple sites without the copyright holder's express written permission. Additionally, content may not be used with any artificial intelligence tools or machine learning technologies. However, users may print, download, or email articles for individual use. This abstract may be abridged. No warranty is given about the accuracy of the copy. Users should refer to the original published version of the material for the full abstract.</i> (Copyright applies to all Abstracts.) |
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| RecordInfo | BibRecord: BibEntity: Identifiers: – Type: doi Value: 10.1016/j.camwa.2026.04.029 Languages: – Code: eng Text: English PhysicalDescription: Pagination: PageCount: 20 StartPage: 135 Subjects: – SubjectFull: Domain decomposition methods Type: general – SubjectFull: Multigrid methods (Numerical analysis) Type: general – SubjectFull: Algorithms Type: general – SubjectFull: Convex programming Type: general – SubjectFull: Imaging systems Type: general – SubjectFull: Partial differential equations Type: general Titles: – TitleFull: Randomized subspace correction methods for convex optimization. Type: main BibRelationships: HasContributorRelationships: – PersonEntity: Name: NameFull: Jiang, Boou – PersonEntity: Name: NameFull: Park, Jongho – PersonEntity: Name: NameFull: Xu, Jinchao IsPartOfRelationships: – BibEntity: Dates: – D: 01 M: 08 Text: Aug2026 Type: published Y: 2026 Identifiers: – Type: issn-print Value: 08981221 Numbering: – Type: volume Value: 215 Titles: – TitleFull: Computers & Mathematics with Applications Type: main |
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