Quantitative Convergence of a Discretization of Dynamic Optimal Transport Using the Dual Formulation.
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| Title: | Quantitative Convergence of a Discretization of Dynamic Optimal Transport Using the Dual Formulation. |
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| Authors: | Ishida, Sadashige1 (AUTHOR) sadashige.ishida@ist.ac.at, Lavenant, Hugo2 (AUTHOR) hugo.lavenant@unibocconi.it |
| Source: | Foundations of Computational Mathematics. Feb2026, Vol. 26 Issue 1, p349-384. 36p. |
| Subjects: | Discretization methods, Duality theory (Mathematics), Hamilton-Jacobi equations, Vector fields |
| Abstract: | We present a discretization of the dynamic optimal transport problem for which we can obtain the convergence rate for the value of the transport cost to its continuous value when the temporal and spatial stepsize vanish. This convergence result does not require any regularity assumption on the measures, though experiments suggest that the rate is not sharp. Via an analysis of the duality gap we also obtain the convergence rates for the gradient of the optimal potentials and the velocity field under mild regularity assumptions. To obtain such rates, we discretize the dual formulation of the dynamic optimal transport problem and use the mature literature related to the error due to discretizing the Hamilton–Jacobi equation. [ABSTRACT FROM AUTHOR] |
| Copyright of Foundations of Computational Mathematics 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: 192095343 AccessLevel: 6 PubType: Academic Journal PubTypeId: academicJournal PreciseRelevancyScore: 0 |
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| Items | – Name: Title Label: Title Group: Ti Data: Quantitative Convergence of a Discretization of Dynamic Optimal Transport Using the Dual Formulation. – Name: Author Label: Authors Group: Au Data: <searchLink fieldCode="AR" term="%22Ishida%2C+Sadashige%22">Ishida, Sadashige</searchLink><relatesTo>1</relatesTo> (AUTHOR)<i> sadashige.ishida@ist.ac.at</i><br /><searchLink fieldCode="AR" term="%22Lavenant%2C+Hugo%22">Lavenant, Hugo</searchLink><relatesTo>2</relatesTo> (AUTHOR)<i> hugo.lavenant@unibocconi.it</i> – Name: TitleSource Label: Source Group: Src Data: <searchLink fieldCode="JN" term="%22Foundations+of+Computational+Mathematics%22">Foundations of Computational Mathematics</searchLink>. Feb2026, Vol. 26 Issue 1, p349-384. 36p. – Name: Subject Label: Subjects Group: Su Data: <searchLink fieldCode="DE" term="%22Discretization+methods%22">Discretization methods</searchLink><br /><searchLink fieldCode="DE" term="%22Duality+theory+%28Mathematics%29%22">Duality theory (Mathematics)</searchLink><br /><searchLink fieldCode="DE" term="%22Hamilton-Jacobi+equations%22">Hamilton-Jacobi equations</searchLink><br /><searchLink fieldCode="DE" term="%22Vector+fields%22">Vector fields</searchLink> – Name: Abstract Label: Abstract Group: Ab Data: We present a discretization of the dynamic optimal transport problem for which we can obtain the convergence rate for the value of the transport cost to its continuous value when the temporal and spatial stepsize vanish. This convergence result does not require any regularity assumption on the measures, though experiments suggest that the rate is not sharp. Via an analysis of the duality gap we also obtain the convergence rates for the gradient of the optimal potentials and the velocity field under mild regularity assumptions. To obtain such rates, we discretize the dual formulation of the dynamic optimal transport problem and use the mature literature related to the error due to discretizing the Hamilton–Jacobi equation. [ABSTRACT FROM AUTHOR] – Name: AbstractSuppliedCopyright Label: Group: Ab Data: <i>Copyright of Foundations of Computational Mathematics 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/s10208-024-09686-3 Languages: – Code: eng Text: English PhysicalDescription: Pagination: PageCount: 36 StartPage: 349 Subjects: – SubjectFull: Discretization methods Type: general – SubjectFull: Duality theory (Mathematics) Type: general – SubjectFull: Hamilton-Jacobi equations Type: general – SubjectFull: Vector fields Type: general Titles: – TitleFull: Quantitative Convergence of a Discretization of Dynamic Optimal Transport Using the Dual Formulation. Type: main BibRelationships: HasContributorRelationships: – PersonEntity: Name: NameFull: Ishida, Sadashige – PersonEntity: Name: NameFull: Lavenant, Hugo IsPartOfRelationships: – BibEntity: Dates: – D: 01 M: 02 Text: Feb2026 Type: published Y: 2026 Identifiers: – Type: issn-print Value: 16153375 Numbering: – Type: volume Value: 26 – Type: issue Value: 1 Titles: – TitleFull: Foundations of Computational Mathematics Type: main |
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