On optimal transport of matrix-valued measures
Optimization and Control
2019-07-16 v2 Functional Analysis
Metric Geometry
Abstract
We suggest a new way of defining optimal transport of positive-semidefinite matrix-valued measures. It is inspired by a recent rendering of the incompressible Euler equations and related conservative systems as concave maximization problems. The main object of our attention is the Kantorovich-Bures metric space, which is a matricial analogue of the Wasserstein and Hellinger-Kantorovich metric spaces. We establish some topological, metric and geometric properties of this space, which includes the existence of the optimal transportation path.
Keywords
Cite
@article{arxiv.1808.05064,
title = {On optimal transport of matrix-valued measures},
author = {Yann Brenier and Dmitry Vorotnikov},
journal= {arXiv preprint arXiv:1808.05064},
year = {2019}
}