An Adaptive Parameter-free and Projection-free Restarting Level Set Method for Constrained Convex Optimization Under the Error Bound Condition.
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| Title: | An Adaptive Parameter-free and Projection-free Restarting Level Set Method for Constrained Convex Optimization Under the Error Bound Condition. |
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| Authors: | Lin, Qihang1 QIHANG-LIN@UIOWA.EDU, Soheili, Negar2 NAZAD@UIC.EDU, Ma, Runchao1 RUNCHAO-MA@UIOWA.EDU, Nadarajah, Selvaprabu2 SELVAN@UIC.EDU |
| Source: | Journal of Machine Learning Research. Jan-Dec2025, Vol. 26, p1-45. 45p. |
| Subjects: | Constrained optimization, Subgradient methods, Mathematical optimization, Optimization algorithms |
| Abstract: | Recent efforts to accelerate first-order methods have focused on convex optimization problems that satisfy a geometric property known as error-bound condition, which covers a broad class of problems, including piece-wise linear programs and strongly convex programs. Parameter-free first-order methods that employ projection-free updates have the potential to broaden the benefit of acceleration. Such a method has been developed for unconstrained convex optimization but is lacking for general constrained convex optimization. We propose a parameter-free level-set method for the latter constrained case based on projection-free subgradient method that exhibits accelerated convergence for problems that satisfy an errorbound condition. Our method maintains a separate copy of the level-set sub-problem for each level parameter value and restarts the computation of these copies based on objective function progress. Applying such a restarting scheme in a level-set context is novel and results in an algorithm that dynamically adapts the precision of each copy. This property is key to extending prior restarting methods based on static precision that have been proposed for unconstrained convex optimization to handle constraints. We report promising numerical performance relative to benchmark methods. [ABSTRACT FROM AUTHOR] |
| Copyright of Journal of Machine Learning Research is the property of Microtome Publishing 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: 193647797 AccessLevel: 6 PubType: Academic Journal PubTypeId: academicJournal PreciseRelevancyScore: 0 |
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| Items | – Name: Title Label: Title Group: Ti Data: An Adaptive Parameter-free and Projection-free Restarting Level Set Method for Constrained Convex Optimization Under the Error Bound Condition. – Name: Author Label: Authors Group: Au Data: <searchLink fieldCode="AR" term="%22Lin%2C+Qihang%22">Lin, Qihang</searchLink><relatesTo>1</relatesTo><i> QIHANG-LIN@UIOWA.EDU</i><br /><searchLink fieldCode="AR" term="%22Soheili%2C+Negar%22">Soheili, Negar</searchLink><relatesTo>2</relatesTo><i> NAZAD@UIC.EDU</i><br /><searchLink fieldCode="AR" term="%22Ma%2C+Runchao%22">Ma, Runchao</searchLink><relatesTo>1</relatesTo><i> RUNCHAO-MA@UIOWA.EDU</i><br /><searchLink fieldCode="AR" term="%22Nadarajah%2C+Selvaprabu%22">Nadarajah, Selvaprabu</searchLink><relatesTo>2</relatesTo><i> SELVAN@UIC.EDU</i> – Name: TitleSource Label: Source Group: Src Data: <searchLink fieldCode="JN" term="%22Journal+of+Machine+Learning+Research%22">Journal of Machine Learning Research</searchLink>. Jan-Dec2025, Vol. 26, p1-45. 45p. – Name: Subject Label: Subjects Group: Su Data: <searchLink fieldCode="DE" term="%22Constrained+optimization%22">Constrained optimization</searchLink><br /><searchLink fieldCode="DE" term="%22Subgradient+methods%22">Subgradient methods</searchLink><br /><searchLink fieldCode="DE" term="%22Mathematical+optimization%22">Mathematical optimization</searchLink><br /><searchLink fieldCode="DE" term="%22Optimization+algorithms%22">Optimization algorithms</searchLink> – Name: Abstract Label: Abstract Group: Ab Data: Recent efforts to accelerate first-order methods have focused on convex optimization problems that satisfy a geometric property known as error-bound condition, which covers a broad class of problems, including piece-wise linear programs and strongly convex programs. Parameter-free first-order methods that employ projection-free updates have the potential to broaden the benefit of acceleration. Such a method has been developed for unconstrained convex optimization but is lacking for general constrained convex optimization. We propose a parameter-free level-set method for the latter constrained case based on projection-free subgradient method that exhibits accelerated convergence for problems that satisfy an errorbound condition. Our method maintains a separate copy of the level-set sub-problem for each level parameter value and restarts the computation of these copies based on objective function progress. Applying such a restarting scheme in a level-set context is novel and results in an algorithm that dynamically adapts the precision of each copy. This property is key to extending prior restarting methods based on static precision that have been proposed for unconstrained convex optimization to handle constraints. We report promising numerical performance relative to benchmark methods. [ABSTRACT FROM AUTHOR] – Name: AbstractSuppliedCopyright Label: Group: Ab Data: <i>Copyright of Journal of Machine Learning Research is the property of Microtome Publishing 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: Languages: – Code: eng Text: English PhysicalDescription: Pagination: PageCount: 45 StartPage: 1 Subjects: – SubjectFull: Constrained optimization Type: general – SubjectFull: Subgradient methods Type: general – SubjectFull: Mathematical optimization Type: general – SubjectFull: Optimization algorithms Type: general Titles: – TitleFull: An Adaptive Parameter-free and Projection-free Restarting Level Set Method for Constrained Convex Optimization Under the Error Bound Condition. Type: main BibRelationships: HasContributorRelationships: – PersonEntity: Name: NameFull: Lin, Qihang – PersonEntity: Name: NameFull: Soheili, Negar – PersonEntity: Name: NameFull: Ma, Runchao – PersonEntity: Name: NameFull: Nadarajah, Selvaprabu IsPartOfRelationships: – BibEntity: Dates: – D: 01 M: 01 Text: Jan-Dec2025 Type: published Y: 2025 Identifiers: – Type: issn-print Value: 15324435 Numbering: – Type: volume Value: 26 Titles: – TitleFull: Journal of Machine Learning Research Type: main |
| ResultId | 1 |
