| Issue |
ESAIM: M2AN
Volume 49, Number 6, November-December 2015
Special Issue - Optimal Transport
|
|
|---|---|---|
| Page(s) | 1621 - 1642 | |
| DOI | https://doi.org/10.1051/m2an/2015033 | |
| Published online | 05 November 2015 | |
Numerical methods for matching for teams and Wasserstein barycenters
1 CEREMADE, UMR CNRS 7534, Université Paris IX Dauphine, Pl. de
Lattre de Tassigny, 75775 Paris cedex 16, France.
carlier@ceremade.dauphine.fr
2 Department of Mathematics and Statistics, McGill University,
805 Sherbrooke Street West, Montreal, Canada.
adam.oberman@mcgill.ca
3 Laboratoire Jean Kuntzmann, Université Joseph Fourier, Tour
IRMA, BP 53 51, rue des Mathématiques 38041 Grenoble cedex 9, France.
edouard.oudet@imag.fr
Received:
24
April
2015
Equilibrium multi-population matching (matching for teams) is a problem from mathematical economics which is related to multi-marginal optimal transport. A special but important case is the Wasserstein barycenter problem, which has applications in image processing and statistics. Two algorithms are presented: a linear programming algorithm and an efficient 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 efficiency of the algorithms.
Mathematics Subject Classification: 49M29 / 90C05
Key words: Matching for teams / Wasserstein barycenters / duality / linear programming / numerical methods for nonsmooth convex minimization
© EDP Sciences, SMAI 2015
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