Numerical methods for matching for teams and Wasserstein barycenters
Carlier, Guillaume; Oberman, Adam; Oudet, Edouard (2015), Numerical methods for matching for teams and Wasserstein barycenters, Modélisation mathématique et analyse numérique, 49, 6, p. 1621-1642. 10.1051/m2an/2015033
Type
Article accepté pour publication ou publiéExternal document link
https://arxiv.org/abs/1411.3602v1Date
2015Journal name
Modélisation mathématique et analyse numériqueVolume
49Number
6Publisher
AFCET
Pages
1621-1642
Publication identifier
Metadata
Show full item recordAbstract (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.Subjects / Keywords
Wasserstein barycenter; duality; matching for teams; linear programming; numerical methods for nonsmooth convex minimizationRelated items
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