• xmlui.mirage2.page-structure.header.title
    • français
    • English
  • Help
  • Login
  • Language 
    • Français
    • English
View Item 
  •   BIRD Home
  • CEREMADE (UMR CNRS 7534)
  • CEREMADE : Publications
  • View Item
  •   BIRD Home
  • CEREMADE (UMR CNRS 7534)
  • CEREMADE : Publications
  • View Item
JavaScript is disabled for your browser. Some features of this site may not work without it.

Browse

BIRDResearch centres & CollectionsBy Issue DateAuthorsTitlesTypeThis CollectionBy Issue DateAuthorsTitlesType

My Account

LoginRegister

Statistics

Most Popular ItemsStatistics by CountryMost Popular Authors
Thumbnail

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

Benamou, Jean-David; Gallouët, Thomas; Vialard, François-Xavier (2019), Second order models for optimal transport and cubic splines on the Wasserstein space, Foundations of Computational Mathematics, 19, p. 1113–1143. 10.1007/s10208-019-09425-z

View/Open
SplinesWasserstein_final(1).pdf (1.289Mb)
Type
Article accepté pour publication ou publié
Date
2019
Journal name
Foundations of Computational Mathematics
Number
19
Publisher
Springer
Pages
1113–1143
Publication identifier
10.1007/s10208-019-09425-z
Metadata
Show full item record
Author(s)
Benamou, Jean-David
CEntre de REcherches en MAthématiques de la DEcision [CEREMADE]
Gallouët, Thomas
CEntre de REcherches en MAthématiques de la DEcision [CEREMADE]
Vialard, François-Xavier
CEntre de REcherches en MAthématiques de la DEcision [CEREMADE]
Abstract (EN)
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 simpler approach, similarly to Brenier's generalized Euler solutions. Our method is based on the relaxation of the variational problem on the path space. We propose an efficient implementation based on multimarginal optimal transport and entropic regularization in 1D and 2D. Our framework also enables extrapolation in the Wasserstein geodesic via a natural convex relaxation.
Subjects / Keywords
multimarginal optimal transport; Wasserstein; Cubic splines

Related items

Showing items related by title and author.

  • Thumbnail
    A Second-Order Model for Time-Dependent Data Interpolation: Splines on Shape Spaces 
    Vialard, François-Xavier; Trouvé, Alain (2010) Communication / Conférence
  • Thumbnail
    Extension to Infinite Dimensions of a Stochastic Second-Order Model associated with the Shape Splines 
    Vialard, François-Xavier (2013) Article accepté pour publication ou publié
  • Thumbnail
    Shape Splines and Stochastic Shape Evolutions: A Second Order Point of View 
    Trouvé, Alain; Vialard, François-Xavier (2012) Article accepté pour publication ou publié
  • Thumbnail
    Generalized compressible fluid flows and solutions of the Camassa-Holm variational model 
    Gallouët, Thomas; Natale, Andrea; Vialard, François-Xavier (2018) Document de travail / Working paper
  • Thumbnail
    A Second-order Total Variation Metric on the Space of Immersed Curves 
    Vialard, François-Xavier; Peyré, Gabriel; Nardi, Giacomo (2014) Document de travail / Working paper
Dauphine PSL Bibliothèque logo
Place du Maréchal de Lattre de Tassigny 75775 Paris Cedex 16
Phone: 01 44 05 40 94
Contact
Dauphine PSL logoEQUIS logoCreative Commons logo