• français
    • English
  • English 
    • français
    • English
  • Login
JavaScript is disabled for your browser. Some features of this site may not work without it.
BIRD Home

Browse

This CollectionBy Issue DateAuthorsTitlesSubjectsJournals BIRDResearch centres & CollectionsBy Issue DateAuthorsTitlesSubjectsJournals

My Account

Login

Statistics

View Usage Statistics

Iterative Bregman Projections for Regularized Transportation Problems

Thumbnail
Date
2015
Publisher city
Paris
Link to item file
https://arxiv.org/abs/1412.5154v1
Dewey
Analyse
Sujet
Kullback-Leibler Bregman divergence projection; Transportation Problems; Iterative Bregman Projections
Journal issue
SIAM Journal on Scientific Computing
Volume
37
Number
2
Publication date
2015
Article pages
A1111–A1138
Publisher
SIAM - Society for Industrial and Applied Mathematics
DOI
http://dx.doi.org/10.1137/141000439
URI
https://basepub.dauphine.fr/handle/123456789/14715
Collections
  • CEREMADE : Publications
Metadata
Show full item record
Author
Benamou, Jean-David
Carlier, Guillaume
Cuturi, Marco
Nenna, Luca
Peyré, Gabriel
Type
Article accepté pour publication ou publié
Abstract (EN)
This article details a general numerical framework to approximate so-lutions to linear programs related to optimal transport. The general idea is to introduce an entropic regularization of the initial linear program. This regularized problem corresponds to a Kullback-Leibler Bregman di-vergence projection of a vector (representing some initial joint distribu-tion) on the polytope of constraints. We show that for many problems related to optimal transport, the set of linear constraints can be split in an intersection of a few simple constraints, for which the projections can be computed in closed form. This allows us to make use of iterative Bregman projections (when there are only equality constraints) or more generally Bregman-Dykstra iterations (when inequality constraints are in-volved). We illustrate the usefulness of this approach to several variational problems related to optimal transport: barycenters for the optimal trans-port metric, tomographic reconstruction, multi-marginal optimal trans-port and in particular its application to Brenier's relaxed solutions of in-compressible Euler equations, partial un-balanced optimal transport and optimal transport with capacity constraints.

  • Accueil Bibliothèque
  • Site de l'Université Paris-Dauphine
  • Contact
SCD Paris Dauphine - Place du Maréchal de Lattre de Tassigny 75775 Paris Cedex 16

 Content on this site is licensed under a Creative Commons 2.0 France (CC BY-NC-ND 2.0) license.