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Numerical methods for matching for teams and Wasserstein barycenters

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Date
2015
Link to item file
https://arxiv.org/abs/1411.3602v1
Dewey
Probabilités et mathématiques appliquées
Sujet
Wasserstein barycenter; duality; matching for teams; linear programming; numerical methods for nonsmooth convex minimization
Journal issue
Modélisation mathématique et analyse numérique
Volume
49
Number
6
Publication date
2015
Article pages
1621-1642
Publisher
AFCET
DOI
http://dx.doi.org/10.1051/m2an/2015033
URI
https://basepub.dauphine.fr/handle/123456789/13300
Collections
  • CEREMADE : Publications
Metadata
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Author
Carlier, Guillaume
Oberman, Adam
Oudet, Edouard
Type
Article accepté pour publication ou publié
Abstract (EN)
Equilibrium multi-population matching (matching for teams) is a prob- lem from mathematical economics which is related to multi-marginal op- timal transport. A special but important case is the Wasserstein barycen- ter problem, which has applications in image processing and statistics. Two algorithms are presented: a linear programming algorithm and an e cient nonsmooth optimization algorithm, which applies in the case of the Wasserstein barycenters. The measures are approximated by discrete measures: convergence of the approximation is proved. Numerical results are presented which illustrate the e ciency of the algorithms.

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