Geodesic
Numerical methods for matching for teams and Wasserstein barycenters
Carlier, Guillaume1  ; Oberman, Adam2 ; Oudet, Edouard3 
1 CEREMADE, UMR CNRS 7534, Université Paris IX Dauphine, Pl. de Lattre de Tassigny, 75775 Paris cedex 16, France.
2 Department of Mathematics and Statistics, McGill University, 805 Sherbrooke Street West, Montreal, Canada.
3 Laboratoire Jean Kuntzmann, Université Joseph Fourier, Tour IRMA, BP 53 51, rue des Mathématiques 38041 Grenoble cedex 9, France.
ESAIM: Mathematical Modelling and Numerical Analysis , Optimal Transport, Tome 49 (2015) no. 6, pp. 1621-1642

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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.

Reçu le :
DOI : 10.1051/m2an/2015033
Classification : 49M29, 90C05
Keywords: Matching for teams, Wasserstein barycenters, duality, linear programming, numerical methods for nonsmooth convex minimization

Carlier, Guillaume 1 ; Oberman, Adam 2 ; Oudet, Edouard 3

1 CEREMADE, UMR CNRS 7534, Université Paris IX Dauphine, Pl. de Lattre de Tassigny, 75775 Paris cedex 16, France.
2 Department of Mathematics and Statistics, McGill University, 805 Sherbrooke Street West, Montreal, Canada.
3 Laboratoire Jean Kuntzmann, Université Joseph Fourier, Tour IRMA, BP 53 51, rue des Mathématiques 38041 Grenoble cedex 9, France. 
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     title = {Numerical methods for matching for teams and {Wasserstein} barycenters},
     journal = {ESAIM: Mathematical Modelling and Numerical Analysis },
     pages = {1621--1642},
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Carlier, Guillaume; Oberman, Adam; Oudet, Edouard. Numerical methods for matching for teams and Wasserstein barycenters. ESAIM: Mathematical Modelling and Numerical Analysis , Optimal Transport, Tome 49 (2015) no. 6, pp. 1621-1642. doi: 10.1051/m2an/2015033

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