Convergence rates for sums-of-squares hierarchies with correlative sparsity.
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| Title: | Convergence rates for sums-of-squares hierarchies with correlative sparsity. |
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| Authors: | Korda, Milan1,2 (AUTHOR) korda@laas.fr, Magron, Victor1 (AUTHOR) vmagron@laas.fr, Ríos-Zertuche, Rodolfo3 (AUTHOR) rodolforiosz@gmail.com |
| Source: | Mathematical Programming. Jan2025, Vol. 209 Issue 1, p435-473. 39p. |
| Subjects: | Interior-point methods, Semialgebraic sets, Polynomials |
| Abstract: | This work derives upper bounds on the convergence rate of the moment-sum-of-squares hierarchy with correlative sparsity for global minimization of polynomials on compact basic semialgebraic sets. The main conclusion is that both sparse hierarchies based on the Schmüdgen and Putinar Positivstellensätze enjoy a polynomial rate of convergence that depends on the size of the largest clique in the sparsity graph but not on the ambient dimension. Interestingly, the sparse bounds outperform the best currently available bounds for the dense hierarchy when the maximum clique size is sufficiently small compared to the ambient dimension and the performance is measured by the running time of an interior point method required to obtain a bound on the global minimum of a given accuracy. [ABSTRACT FROM AUTHOR] |
| Copyright of Mathematical Programming 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: 182239570 AccessLevel: 6 PubType: Academic Journal PubTypeId: academicJournal PreciseRelevancyScore: 0 |
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| Items | – Name: Title Label: Title Group: Ti Data: Convergence rates for sums-of-squares hierarchies with correlative sparsity. – Name: Author Label: Authors Group: Au Data: <searchLink fieldCode="AR" term="%22Korda%2C+Milan%22">Korda, Milan</searchLink><relatesTo>1,2</relatesTo> (AUTHOR)<i> korda@laas.fr</i><br /><searchLink fieldCode="AR" term="%22Magron%2C+Victor%22">Magron, Victor</searchLink><relatesTo>1</relatesTo> (AUTHOR)<i> vmagron@laas.fr</i><br /><searchLink fieldCode="AR" term="%22Ríos-Zertuche%2C+Rodolfo%22">Ríos-Zertuche, Rodolfo</searchLink><relatesTo>3</relatesTo> (AUTHOR)<i> rodolforiosz@gmail.com</i> – Name: TitleSource Label: Source Group: Src Data: <searchLink fieldCode="JN" term="%22Mathematical+Programming%22">Mathematical Programming</searchLink>. Jan2025, Vol. 209 Issue 1, p435-473. 39p. – Name: Subject Label: Subjects Group: Su Data: <searchLink fieldCode="DE" term="%22Interior-point+methods%22">Interior-point methods</searchLink><br /><searchLink fieldCode="DE" term="%22Semialgebraic+sets%22">Semialgebraic sets</searchLink><br /><searchLink fieldCode="DE" term="%22Polynomials%22">Polynomials</searchLink> – Name: Abstract Label: Abstract Group: Ab Data: This work derives upper bounds on the convergence rate of the moment-sum-of-squares hierarchy with correlative sparsity for global minimization of polynomials on compact basic semialgebraic sets. The main conclusion is that both sparse hierarchies based on the Schmüdgen and Putinar Positivstellensätze enjoy a polynomial rate of convergence that depends on the size of the largest clique in the sparsity graph but not on the ambient dimension. Interestingly, the sparse bounds outperform the best currently available bounds for the dense hierarchy when the maximum clique size is sufficiently small compared to the ambient dimension and the performance is measured by the running time of an interior point method required to obtain a bound on the global minimum of a given accuracy. [ABSTRACT FROM AUTHOR] – Name: AbstractSuppliedCopyright Label: Group: Ab Data: <i>Copyright of Mathematical Programming 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.) |
| PLink | https://search.ebscohost.com/login.aspx?direct=true&site=eds-live&db=egs&AN=182239570 |
| RecordInfo | BibRecord: BibEntity: Identifiers: – Type: doi Value: 10.1007/s10107-024-02071-6 Languages: – Code: eng Text: English PhysicalDescription: Pagination: PageCount: 39 StartPage: 435 Subjects: – SubjectFull: Interior-point methods Type: general – SubjectFull: Semialgebraic sets Type: general – SubjectFull: Polynomials Type: general Titles: – TitleFull: Convergence rates for sums-of-squares hierarchies with correlative sparsity. Type: main BibRelationships: HasContributorRelationships: – PersonEntity: Name: NameFull: Korda, Milan – PersonEntity: Name: NameFull: Magron, Victor – PersonEntity: Name: NameFull: Ríos-Zertuche, Rodolfo IsPartOfRelationships: – BibEntity: Dates: – D: 01 M: 01 Text: Jan2025 Type: published Y: 2025 Identifiers: – Type: issn-print Value: 00255610 Numbering: – Type: volume Value: 209 – Type: issue Value: 1 Titles: – TitleFull: Mathematical Programming Type: main |
| ResultId | 1 |
