Résumé en anglais

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.