Invariance properties of the Monge-Kantorovich mass transport problem
Analysis of PDEs
2015-04-22 v2
Abstract
We consider the multidimensional Monge-Kantrovich transport problem in an abstract setting. Our main results state that if a cost function and marginal measures are invariant by a family of transformations, then a solution of the Kantrovich relaxation problem and a solution of its dual can be chosen so that they are invariant under the same family of transformations. This provides a new tool to study and analyze the support of optimal transport plans and consequently to scrutinize the Monge problem. Birkhoff's Ergodic theorem is an essential tool in our analysis.
Keywords
Cite
@article{arxiv.1311.7051,
title = {Invariance properties of the Monge-Kantorovich mass transport problem},
author = {Abbas Moameni},
journal= {arXiv preprint arXiv:1311.7051},
year = {2015}
}