Rank-one approximation of a higher-order tensor by a Riemannian trust-region method: Rank-one approximation of a higher-order tensor by a Riemannian...: J. Chen, W. Huang.
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| Title: | Rank-one approximation of a higher-order tensor by a Riemannian trust-region method: Rank-one approximation of a higher-order tensor by a Riemannian...: J. Chen, W. Huang. |
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| Authors: | Chen, Jianheng1,2 (AUTHOR) cjh868@126.com, Huang, Wen2 (AUTHOR) wen.huang@xmu.edu.cn |
| Source: | Computational Optimization & Applications. Mar2025, Vol. 90 Issue 2, p515-556. 42p. |
| Subjects: | Computational mathematics, Tangent function, Vector valued functions |
| Abstract: | In this paper, we consider a rank-one approximation problem of a higher-order tensor. We treat the problem as an optimization model on a Cartesian product of manifolds and solve this model by using a Riemannian optimization method. We derive the action of the Riemannian Hessian of the objective function on tangent vectors to the Cartesian product of manifolds. A Riemannian trust-region method with block-diagonal Hessian is used to solve this model, and the subproblem is solved by the truncated conjugate gradient method. The convergence analysis of the Riemannian trust-region method has been established in the literature with certain assumptions. We verify those assumptions for the rank-one approximation problem. Numerical experiments illustrate that the proposed model with the method is feasible and effective. [ABSTRACT FROM AUTHOR] |
| Copyright of Computational Optimization & Applications is the property of Springer Nature 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: 183372640 AccessLevel: 6 PubType: Academic Journal PubTypeId: academicJournal PreciseRelevancyScore: 0 |
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| Items | – Name: Title Label: Title Group: Ti Data: Rank-one approximation of a higher-order tensor by a Riemannian trust-region method: Rank-one approximation of a higher-order tensor by a Riemannian...: J. Chen, W. Huang. – Name: Author Label: Authors Group: Au Data: <searchLink fieldCode="AR" term="%22Chen%2C+Jianheng%22">Chen, Jianheng</searchLink><relatesTo>1,2</relatesTo> (AUTHOR)<i> cjh868@126.com</i><br /><searchLink fieldCode="AR" term="%22Huang%2C+Wen%22">Huang, Wen</searchLink><relatesTo>2</relatesTo> (AUTHOR)<i> wen.huang@xmu.edu.cn</i> – Name: TitleSource Label: Source Group: Src Data: <searchLink fieldCode="JN" term="%22Computational+Optimization+%26+Applications%22">Computational Optimization & Applications</searchLink>. Mar2025, Vol. 90 Issue 2, p515-556. 42p. – Name: Subject Label: Subjects Group: Su Data: <searchLink fieldCode="DE" term="%22Computational+mathematics%22">Computational mathematics</searchLink><br /><searchLink fieldCode="DE" term="%22Tangent+function%22">Tangent function</searchLink><br /><searchLink fieldCode="DE" term="%22Vector+valued+functions%22">Vector valued functions</searchLink> – Name: Abstract Label: Abstract Group: Ab Data: In this paper, we consider a rank-one approximation problem of a higher-order tensor. We treat the problem as an optimization model on a Cartesian product of manifolds and solve this model by using a Riemannian optimization method. We derive the action of the Riemannian Hessian of the objective function on tangent vectors to the Cartesian product of manifolds. A Riemannian trust-region method with block-diagonal Hessian is used to solve this model, and the subproblem is solved by the truncated conjugate gradient method. The convergence analysis of the Riemannian trust-region method has been established in the literature with certain assumptions. We verify those assumptions for the rank-one approximation problem. Numerical experiments illustrate that the proposed model with the method is feasible and effective. [ABSTRACT FROM AUTHOR] – Name: AbstractSuppliedCopyright Label: Group: Ab Data: <i>Copyright of Computational Optimization & Applications is the property of Springer Nature 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: 10.1007/s10589-024-00634-z Languages: – Code: eng Text: English PhysicalDescription: Pagination: PageCount: 42 StartPage: 515 Subjects: – SubjectFull: Computational mathematics Type: general – SubjectFull: Tangent function Type: general – SubjectFull: Vector valued functions Type: general Titles: – TitleFull: Rank-one approximation of a higher-order tensor by a Riemannian trust-region method: Rank-one approximation of a higher-order tensor by a Riemannian...: J. Chen, W. Huang. Type: main BibRelationships: HasContributorRelationships: – PersonEntity: Name: NameFull: Chen, Jianheng – PersonEntity: Name: NameFull: Huang, Wen IsPartOfRelationships: – BibEntity: Dates: – D: 01 M: 03 Text: Mar2025 Type: published Y: 2025 Identifiers: – Type: issn-print Value: 09266003 Numbering: – Type: volume Value: 90 – Type: issue Value: 2 Titles: – TitleFull: Computational Optimization & Applications Type: main |
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