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Article Dans Une Revue ESAIM: Mathematical Modelling and Numerical Analysis Année : 2015

Numerical methods for matching for teams and Wasserstein barycenters

Résumé

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.
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Dates et versions

hal-00987292 , version 1 (05-05-2014)

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Guillaume Carlier, Adam Oberman, Edouard Oudet. Numerical methods for matching for teams and Wasserstein barycenters. ESAIM: Mathematical Modelling and Numerical Analysis, 2015, Special Issue - Optimal Transport, 49 (6), pp.1621-1642. ⟨10.1051/m2an/2015033⟩. ⟨hal-00987292⟩
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