Barycenters in generalized Wasserstein spaces

Nhan-Phu Chung, Thanh-Son Trinh

Published 2019-09-12Version 1

In 2014, Piccoli and Rossi introduced generalized Wasserstein spaces which are combinations of Wasserstein distances and $L^1$-distances [11]. In this article, we follow the ideas of Agueh and Carlier [1] to study generalized Wasserstein barycenters. We show the existence of barycenters for measures with compact supports. We also investigate a dual problem of the barycenter problem via our Kantorovich duality formula for generalized Wasserstein distances. Finally, we provide consistency of the barycenters.