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Second order models for optimal transport and cubic splines on the Wasserstein space

Abstract : On the space of probability densities, we extend the Wasserstein geodesics to the case of higher-order interpolation such as cubic spline interpolation. After presenting the natural extension of cubic splines to the Wasserstein space, we propose a simpler approach based on the relaxation of the variational problem on the path space. We explore two different numerical approaches, one based on multi-marginal optimal transport and entropic regularization and the other based on semi-discrete optimal transport.
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https://hal.archives-ouvertes.fr/hal-01682107
Contributor : François-Xavier Vialard <>
Submitted on : Wednesday, July 25, 2018 - 2:11:58 PM
Last modification on : Wednesday, February 19, 2020 - 8:55:10 AM
Document(s) archivé(s) le : Friday, October 26, 2018 - 2:07:10 PM

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  • HAL Id : hal-01682107, version 2
  • ARXIV : 1801.04144

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Jean-David Benamou, Thomas Gallouët, François-Xavier Vialard. Second order models for optimal transport and cubic splines on the Wasserstein space. Foundations of Computational Mathematics, Springer Verlag, 2019. ⟨hal-01682107v2⟩

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