Academic Journal
AdaBB: Adaptive Barzilai-Borwein Method for Convex Optimization.
| Τίτλος: | AdaBB: Adaptive Barzilai-Borwein Method for Convex Optimization. |
|---|---|
| Συγγραφείς: | Zhou, Danqing1 (AUTHOR) zhoudanqing@smail.nju.edu.cn, Ma, Shiqian2 (AUTHOR) sqma@rice.edu, Yang, Junfeng1 (AUTHOR) jfyang@nju.edu.cn |
| Πηγή: | Mathematics of Operations Research (INFORMS). Feb2026, Vol. 51 Issue 1, p715-745. 31p. |
| Θεματικοί όροι: | Convex programming, Optimization algorithms, Numerical calculations, Nonsmooth optimization, Concave functions, Ergodic theory |
| Περίληψη: | In this paper, we propose AdaBB, an adaptive gradient method based on the Barzilai-Borwein stepsize. The algorithm is line-search-free and parameter-free, and it essentially provides a convergent variant of the Barzilai-Borwein method for general convex optimization problems. We analyze the ergodic convergence of the objective function value and the convergence of the iterates for solving general convex optimization problems. Compared with existing works along this line of research, our algorithm gives the best lower bounds on the stepsize and the average of the stepsizes. Furthermore, we present extensions of the proposed algorithm for solving locally strongly convex and composite convex optimization problems where the objective function is the sum of a smooth function and a nonsmooth function. In the case of local strong convexity, we achieve linear convergence. Our numerical results also demonstrate very promising potential of the proposed algorithms on some representative examples. Funding: S. Ma is supported by the National Science Foundation [Grants DMS-2243650, CCF-2308597, CCF-2311275, and ECCS-2326591] and a startup fund from Rice University. J. Yang is supported by the National Natural Science Foundation of China [Grants 12431011 and 12371301] and the Natural Science Foundation for Distinguished Young Scholars of Gansu Province [Grant 22JR5RA223]. [ABSTRACT FROM AUTHOR] |
| Copyright of Mathematics of Operations Research (INFORMS) is the property of INFORMS: Institute for Operations Research & the Management Sciences 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.) | |
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| Items | – Name: Title Label: Title Group: Ti Data: AdaBB: Adaptive Barzilai-Borwein Method for Convex Optimization. – Name: Author Label: Authors Group: Au Data: <searchLink fieldCode="AR" term="%22Zhou%2C+Danqing%22">Zhou, Danqing</searchLink><relatesTo>1</relatesTo> (AUTHOR)<i> zhoudanqing@smail.nju.edu.cn</i><br /><searchLink fieldCode="AR" term="%22Ma%2C+Shiqian%22">Ma, Shiqian</searchLink><relatesTo>2</relatesTo> (AUTHOR)<i> sqma@rice.edu</i><br /><searchLink fieldCode="AR" term="%22Yang%2C+Junfeng%22">Yang, Junfeng</searchLink><relatesTo>1</relatesTo> (AUTHOR)<i> jfyang@nju.edu.cn</i> – Name: TitleSource Label: Source Group: Src Data: <searchLink fieldCode="JN" term="%22Mathematics+of+Operations+Research+%28INFORMS%29%22">Mathematics of Operations Research (INFORMS)</searchLink>. Feb2026, Vol. 51 Issue 1, p715-745. 31p. – Name: Subject Label: Subject Terms Group: Su Data: <searchLink fieldCode="DE" term="%22Convex+programming%22">Convex programming</searchLink><br /><searchLink fieldCode="DE" term="%22Optimization+algorithms%22">Optimization algorithms</searchLink><br /><searchLink fieldCode="DE" term="%22Numerical+calculations%22">Numerical calculations</searchLink><br /><searchLink fieldCode="DE" term="%22Nonsmooth+optimization%22">Nonsmooth optimization</searchLink><br /><searchLink fieldCode="DE" term="%22Concave+functions%22">Concave functions</searchLink><br /><searchLink fieldCode="DE" term="%22Ergodic+theory%22">Ergodic theory</searchLink> – Name: Abstract Label: Abstract Group: Ab Data: In this paper, we propose AdaBB, an adaptive gradient method based on the Barzilai-Borwein stepsize. The algorithm is line-search-free and parameter-free, and it essentially provides a convergent variant of the Barzilai-Borwein method for general convex optimization problems. We analyze the ergodic convergence of the objective function value and the convergence of the iterates for solving general convex optimization problems. Compared with existing works along this line of research, our algorithm gives the best lower bounds on the stepsize and the average of the stepsizes. Furthermore, we present extensions of the proposed algorithm for solving locally strongly convex and composite convex optimization problems where the objective function is the sum of a smooth function and a nonsmooth function. In the case of local strong convexity, we achieve linear convergence. Our numerical results also demonstrate very promising potential of the proposed algorithms on some representative examples. Funding: S. Ma is supported by the National Science Foundation [Grants DMS-2243650, CCF-2308597, CCF-2311275, and ECCS-2326591] and a startup fund from Rice University. J. Yang is supported by the National Natural Science Foundation of China [Grants 12431011 and 12371301] and the Natural Science Foundation for Distinguished Young Scholars of Gansu Province [Grant 22JR5RA223]. [ABSTRACT FROM AUTHOR] – Name: AbstractSuppliedCopyright Label: Group: Ab Data: <i>Copyright of Mathematics of Operations Research (INFORMS) is the property of INFORMS: Institute for Operations Research & the Management Sciences 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: 10.1287/moor.2024.0510 Languages: – Code: eng Text: English PhysicalDescription: Pagination: PageCount: 31 StartPage: 715 Subjects: – SubjectFull: Convex programming Type: general – SubjectFull: Optimization algorithms Type: general – SubjectFull: Numerical calculations Type: general – SubjectFull: Nonsmooth optimization Type: general – SubjectFull: Concave functions Type: general – SubjectFull: Ergodic theory Type: general Titles: – TitleFull: AdaBB: Adaptive Barzilai-Borwein Method for Convex Optimization. Type: main BibRelationships: HasContributorRelationships: – PersonEntity: Name: NameFull: Zhou, Danqing – PersonEntity: Name: NameFull: Ma, Shiqian – PersonEntity: Name: NameFull: Yang, Junfeng IsPartOfRelationships: – BibEntity: Dates: – D: 01 M: 02 Text: Feb2026 Type: published Y: 2026 Identifiers: – Type: issn-print Value: 0364765X Numbering: – Type: volume Value: 51 – Type: issue Value: 1 Titles: – TitleFull: Mathematics of Operations Research (INFORMS) Type: main |
| ResultId | 1 |