A stochastic first-order trust-region method with inexact restoration for finite-sum minimization.
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| Title: | A stochastic first-order trust-region method with inexact restoration for finite-sum minimization. |
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| Authors: | Bellavia, Stefania1 (AUTHOR), Krejić, Nataša2 (AUTHOR), Morini, Benedetta1 (AUTHOR) benedetta.morini@unifi.it, Rebegoldi, Simone1 (AUTHOR) |
| Source: | Computational Optimization & Applications. Jan2023, Vol. 84 Issue 1, p53-84. 32p. |
| Subjects: | Random functions (Mathematics), Algorithms |
| Abstract: | We propose a stochastic first-order trust-region method with inexact function and gradient evaluations for solving finite-sum minimization problems. Using a suitable reformulation of the given problem, our method combines the inexact restoration approach for constrained optimization with the trust-region procedure and random models. Differently from other recent stochastic trust-region schemes, our proposed algorithm improves feasibility and optimality in a modular way. We provide the expected number of iterations for reaching a near-stationary point by imposing some probability accuracy requirements on random functions and gradients which are, in general, less stringent than the corresponding ones in literature. We validate the proposed algorithm on some nonconvex optimization problems arising in binary classification and regression, showing that it performs well in terms of cost and accuracy, and allows to reduce the burdensome tuning of the hyper-parameters involved. [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: 161138616 AccessLevel: 6 PubType: Academic Journal PubTypeId: academicJournal PreciseRelevancyScore: 0 |
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| Items | – Name: Title Label: Title Group: Ti Data: A stochastic first-order trust-region method with inexact restoration for finite-sum minimization. – Name: Author Label: Authors Group: Au Data: <searchLink fieldCode="AR" term="%22Bellavia%2C+Stefania%22">Bellavia, Stefania</searchLink><relatesTo>1</relatesTo> (AUTHOR)<br /><searchLink fieldCode="AR" term="%22Krejić%2C+Nataša%22">Krejić, Nataša</searchLink><relatesTo>2</relatesTo> (AUTHOR)<br /><searchLink fieldCode="AR" term="%22Morini%2C+Benedetta%22">Morini, Benedetta</searchLink><relatesTo>1</relatesTo> (AUTHOR)<i> benedetta.morini@unifi.it</i><br /><searchLink fieldCode="AR" term="%22Rebegoldi%2C+Simone%22">Rebegoldi, Simone</searchLink><relatesTo>1</relatesTo> (AUTHOR) – Name: TitleSource Label: Source Group: Src Data: <searchLink fieldCode="JN" term="%22Computational+Optimization+%26+Applications%22">Computational Optimization & Applications</searchLink>. Jan2023, Vol. 84 Issue 1, p53-84. 32p. – Name: Subject Label: Subjects Group: Su Data: <searchLink fieldCode="DE" term="%22Random+functions+%28Mathematics%29%22">Random functions (Mathematics)</searchLink><br /><searchLink fieldCode="DE" term="%22Algorithms%22">Algorithms</searchLink> – Name: Abstract Label: Abstract Group: Ab Data: We propose a stochastic first-order trust-region method with inexact function and gradient evaluations for solving finite-sum minimization problems. Using a suitable reformulation of the given problem, our method combines the inexact restoration approach for constrained optimization with the trust-region procedure and random models. Differently from other recent stochastic trust-region schemes, our proposed algorithm improves feasibility and optimality in a modular way. We provide the expected number of iterations for reaching a near-stationary point by imposing some probability accuracy requirements on random functions and gradients which are, in general, less stringent than the corresponding ones in literature. We validate the proposed algorithm on some nonconvex optimization problems arising in binary classification and regression, showing that it performs well in terms of cost and accuracy, and allows to reduce the burdensome tuning of the hyper-parameters involved. [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/s10589-022-00430-7 Languages: – Code: eng Text: English PhysicalDescription: Pagination: PageCount: 32 StartPage: 53 Subjects: – SubjectFull: Random functions (Mathematics) Type: general – SubjectFull: Algorithms Type: general Titles: – TitleFull: A stochastic first-order trust-region method with inexact restoration for finite-sum minimization. Type: main BibRelationships: HasContributorRelationships: – PersonEntity: Name: NameFull: Bellavia, Stefania – PersonEntity: Name: NameFull: Krejić, Nataša – PersonEntity: Name: NameFull: Morini, Benedetta – PersonEntity: Name: NameFull: Rebegoldi, Simone IsPartOfRelationships: – BibEntity: Dates: – D: 01 M: 01 Text: Jan2023 Type: published Y: 2023 Identifiers: – Type: issn-print Value: 09266003 Numbering: – Type: volume Value: 84 – Type: issue Value: 1 Titles: – TitleFull: Computational Optimization & Applications Type: main |
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