Exploiting effective negative curvature directions via SYMMBK algorithm, in Newton–Krylov methods.
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| Title: | Exploiting effective negative curvature directions via SYMMBK algorithm, in Newton–Krylov methods. |
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| Authors: | Fasano, Giovanni1 (AUTHOR) fasano@unive.it, Piermarini, Christian2 (AUTHOR) piermarini@diag.uniroma1.it, Roma, Massimo2 (AUTHOR) roma@diag.uniroma1.it |
| Source: | Computational Optimization & Applications. Jun2025, Vol. 91 Issue 2, p617-647. 31p. |
| Subjects: | Conjugate gradient methods, Computational mathematics, Partial differential equations, Matrix decomposition, Mathematical optimization |
| Abstract: | In this paper we consider the issue of computing negative curvature directions, for nonconvex functions, within Newton–Krylov methods for large scale unconstrained optimization. In the last decades this issue has been widely investigated in the literature, and different approaches have been proposed. We focus on the well known SYMMBK method introduced for solving large scale symmetric possibly indefinite linear systems (Bunch and Kaufman in Math Comput 31:163–179, 2003; Chandra in Conjugate gradient methods for partial differential equations, Yale University, New Haven, 1978; Conn et al. Trust-region methods. MPS-SIAM Series on Optimization, Philadelphia, 2000; HSL 2013: A collection of Fortran codes for large scale scientific computation. http://www.hsl.rl.ac.uk/), and show how to exploit it to yield an effective negative curvature direction in optimization frameworks. The distinguishing feature of our proposal is that the computation of negative curvatures is basically carried out as by–product of SYMMBK procedure, without storing no more than two additional vectors. Hence, no explicit matrix factorization or matrix storage is required. An extensive numerical experimentation has been performed on CUTEst problems; the obtained results have been analyzed also through novel profiles (Quality Profiles) which highlighted the good capability of the algorithms which use negative curvature directions to determine better local minimizers. [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: 185240094 AccessLevel: 6 PubType: Academic Journal PubTypeId: academicJournal PreciseRelevancyScore: 0 |
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| Items | – Name: Title Label: Title Group: Ti Data: Exploiting effective negative curvature directions via SYMMBK algorithm, in Newton–Krylov methods. – Name: Author Label: Authors Group: Au Data: <searchLink fieldCode="AR" term="%22Fasano%2C+Giovanni%22">Fasano, Giovanni</searchLink><relatesTo>1</relatesTo> (AUTHOR)<i> fasano@unive.it</i><br /><searchLink fieldCode="AR" term="%22Piermarini%2C+Christian%22">Piermarini, Christian</searchLink><relatesTo>2</relatesTo> (AUTHOR)<i> piermarini@diag.uniroma1.it</i><br /><searchLink fieldCode="AR" term="%22Roma%2C+Massimo%22">Roma, Massimo</searchLink><relatesTo>2</relatesTo> (AUTHOR)<i> roma@diag.uniroma1.it</i> – Name: TitleSource Label: Source Group: Src Data: <searchLink fieldCode="JN" term="%22Computational+Optimization+%26+Applications%22">Computational Optimization & Applications</searchLink>. Jun2025, Vol. 91 Issue 2, p617-647. 31p. – Name: Subject Label: Subjects Group: Su Data: <searchLink fieldCode="DE" term="%22Conjugate+gradient+methods%22">Conjugate gradient methods</searchLink><br /><searchLink fieldCode="DE" term="%22Computational+mathematics%22">Computational mathematics</searchLink><br /><searchLink fieldCode="DE" term="%22Partial+differential+equations%22">Partial differential equations</searchLink><br /><searchLink fieldCode="DE" term="%22Matrix+decomposition%22">Matrix decomposition</searchLink><br /><searchLink fieldCode="DE" term="%22Mathematical+optimization%22">Mathematical optimization</searchLink> – Name: Abstract Label: Abstract Group: Ab Data: In this paper we consider the issue of computing negative curvature directions, for nonconvex functions, within Newton–Krylov methods for large scale unconstrained optimization. In the last decades this issue has been widely investigated in the literature, and different approaches have been proposed. We focus on the well known SYMMBK method introduced for solving large scale symmetric possibly indefinite linear systems (Bunch and Kaufman in Math Comput 31:163–179, 2003; Chandra in Conjugate gradient methods for partial differential equations, Yale University, New Haven, 1978; Conn et al. Trust-region methods. MPS-SIAM Series on Optimization, Philadelphia, 2000; HSL 2013: A collection of Fortran codes for large scale scientific computation. http://www.hsl.rl.ac.uk/), and show how to exploit it to yield an effective negative curvature direction in optimization frameworks. The distinguishing feature of our proposal is that the computation of negative curvatures is basically carried out as by–product of SYMMBK procedure, without storing no more than two additional vectors. Hence, no explicit matrix factorization or matrix storage is required. An extensive numerical experimentation has been performed on CUTEst problems; the obtained results have been analyzed also through novel profiles (Quality Profiles) which highlighted the good capability of the algorithms which use negative curvature directions to determine better local minimizers. [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/s10589-025-00650-7 Languages: – Code: eng Text: English PhysicalDescription: Pagination: PageCount: 31 StartPage: 617 Subjects: – SubjectFull: Conjugate gradient methods Type: general – SubjectFull: Computational mathematics Type: general – SubjectFull: Partial differential equations Type: general – SubjectFull: Matrix decomposition Type: general – SubjectFull: Mathematical optimization Type: general Titles: – TitleFull: Exploiting effective negative curvature directions via SYMMBK algorithm, in Newton–Krylov methods. Type: main BibRelationships: HasContributorRelationships: – PersonEntity: Name: NameFull: Fasano, Giovanni – PersonEntity: Name: NameFull: Piermarini, Christian – PersonEntity: Name: NameFull: Roma, Massimo IsPartOfRelationships: – BibEntity: Dates: – D: 01 M: 06 Text: Jun2025 Type: published Y: 2025 Identifiers: – Type: issn-print Value: 09266003 Numbering: – Type: volume Value: 91 – Type: issue Value: 2 Titles: – TitleFull: Computational Optimization & Applications Type: main |
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