  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.
