A new inexact gradient descent method with applications to nonsmooth convex optimization.
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| Title: | A new inexact gradient descent method with applications to nonsmooth convex optimization. |
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| Authors: | Khanh, Pham Duy1 (AUTHOR) pdkhanh182@gmail.com, Mordukhovich, Boris S.2 (AUTHOR) aa1086@wayne.edu, Tran, Dat Ba2 (AUTHOR) |
| Source: | Optimization Methods & Software. Apr2026, Vol. 41 Issue 2, p394-422. 29p. |
| Subjects: | Nonsmooth optimization, Convex programming, Mathematical optimization, Optimization algorithms |
| Abstract: | The paper proposes and develops a novel inexact gradient method (IGD) for minimizing $ {\mathcal {C}}^1 $ C 1 -smooth functions with Lipschitzian gradients, i.e. for problems of $ {\mathcal {C}}^{1,1} $ C 1 , 1 optimization. We show that the sequence of gradients generated by IGD converges to zero. The convergence of iterates to stationary points is guaranteed under the Kurdyka-Łojasiewicz (KL) property of the objective function with convergence rates depending on the KL exponent. The newly developed IGD is applied to designing two novel gradient-based methods of nonsmooth convex optimization such as the inexact proximal point methods (GIPPM) and the inexact augmented Lagrangian method (GIALM) for convex programs with linear equality constraints. These two methods inherit global convergence properties from IGD and are confirmed by numerical experiments to have practical advantages over some well-known algorithms of nonsmooth convex optimization. [ABSTRACT FROM AUTHOR] |
| Copyright of Optimization Methods & Software is the property of Taylor & Francis Ltd 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 |
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| Header | DbId: egs DbLabel: Engineering Source An: 193364606 AccessLevel: 6 PubType: Academic Journal PubTypeId: academicJournal PreciseRelevancyScore: 0 |
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| Items | – Name: Title Label: Title Group: Ti Data: A new inexact gradient descent method with applications to nonsmooth convex optimization. – Name: Author Label: Authors Group: Au Data: <searchLink fieldCode="AR" term="%22Khanh%2C+Pham+Duy%22">Khanh, Pham Duy</searchLink><relatesTo>1</relatesTo> (AUTHOR)<i> pdkhanh182@gmail.com</i><br /><searchLink fieldCode="AR" term="%22Mordukhovich%2C+Boris+S%2E%22">Mordukhovich, Boris S.</searchLink><relatesTo>2</relatesTo> (AUTHOR)<i> aa1086@wayne.edu</i><br /><searchLink fieldCode="AR" term="%22Tran%2C+Dat+Ba%22">Tran, Dat Ba</searchLink><relatesTo>2</relatesTo> (AUTHOR) – Name: TitleSource Label: Source Group: Src Data: <searchLink fieldCode="JN" term="%22Optimization+Methods+%26+Software%22">Optimization Methods & Software</searchLink>. Apr2026, Vol. 41 Issue 2, p394-422. 29p. – Name: Subject Label: Subjects Group: Su Data: <searchLink fieldCode="DE" term="%22Nonsmooth+optimization%22">Nonsmooth optimization</searchLink><br /><searchLink fieldCode="DE" term="%22Convex+programming%22">Convex programming</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: The paper proposes and develops a novel inexact gradient method (IGD) for minimizing $ {\mathcal {C}}^1 $ C 1 -smooth functions with Lipschitzian gradients, i.e. for problems of $ {\mathcal {C}}^{1,1} $ C 1 , 1 optimization. We show that the sequence of gradients generated by IGD converges to zero. The convergence of iterates to stationary points is guaranteed under the Kurdyka-Łojasiewicz (KL) property of the objective function with convergence rates depending on the KL exponent. The newly developed IGD is applied to designing two novel gradient-based methods of nonsmooth convex optimization such as the inexact proximal point methods (GIPPM) and the inexact augmented Lagrangian method (GIALM) for convex programs with linear equality constraints. These two methods inherit global convergence properties from IGD and are confirmed by numerical experiments to have practical advantages over some well-known algorithms of nonsmooth convex optimization. [ABSTRACT FROM AUTHOR] – Name: AbstractSuppliedCopyright Label: Group: Ab Data: <i>Copyright of Optimization Methods & Software is the property of Taylor & Francis Ltd 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: 10.1080/10556788.2024.2322700 Languages: – Code: eng Text: English PhysicalDescription: Pagination: PageCount: 29 StartPage: 394 Subjects: – SubjectFull: Nonsmooth optimization Type: general – SubjectFull: Convex programming Type: general – SubjectFull: Mathematical optimization Type: general – SubjectFull: Optimization algorithms Type: general Titles: – TitleFull: A new inexact gradient descent method with applications to nonsmooth convex optimization. Type: main BibRelationships: HasContributorRelationships: – PersonEntity: Name: NameFull: Khanh, Pham Duy – PersonEntity: Name: NameFull: Mordukhovich, Boris S. – PersonEntity: Name: NameFull: Tran, Dat Ba IsPartOfRelationships: – BibEntity: Dates: – D: 01 M: 04 Text: Apr2026 Type: published Y: 2026 Identifiers: – Type: issn-print Value: 10556788 Numbering: – Type: volume Value: 41 – Type: issue Value: 2 Titles: – TitleFull: Optimization Methods & Software Type: main |
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