Numerical methods for matching for teams and Wasserstein barycenters
Numerical Analysis
2014-11-14 v1 Analysis of PDEs
Abstract
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.
Cite
@article{arxiv.1411.3602,
title = {Numerical methods for matching for teams and Wasserstein barycenters},
author = {Guillaume Carlier and Adam Oberman and Edouard Oudet},
journal= {arXiv preprint arXiv:1411.3602},
year = {2014}
}
Comments
29 pages, 13 figures