Numerical methods for matching for teams and Wasserstein barycenters

Carlier, Guillaume; Oberman, Adam; Oudet, Edouard

Carlier, Guillaume; Oberman, Adam; Oudet, Edouard (2015), Numerical methods for matching for teams and Wasserstein barycenters, Modélisation mathématique et analyse numérique, 49, 6, p. 1621-1642. 10.1051/m2an/2015033

Type

Article accepté pour publication ou publié

External document link

https://arxiv.org/abs/1411.3602v1

Date

2015

Journal name

Modélisation mathématique et analyse numérique

Volume

Number

Publisher

AFCET

Pages

1621-1642

Abstract (EN)

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.

Subjects / Keywords

Wasserstein barycenter; duality; matching for teams; linear programming; numerical methods for nonsmooth convex minimization