Transport Problems and Disintegration Maps
Optimization and Control
2012-07-18 v1
Abstract
By disintegration of transport plans it is introduced the notion of transport class. This allows to consider the Monge problem as a particular case of the Kantorovich transport problem, once a transport class is fixed. The transport problem constrained to a fixed transport class is equivalent to an abstract Monge problem over a Wasserstein space of probability measures. Concerning solvability of this kind of constrained problems, it turns out that in some sense the Monge problem corresponds to a lucky case.
Keywords
Cite
@article{arxiv.1207.4026,
title = {Transport Problems and Disintegration Maps},
author = {L. Granieri and F. Maddalena},
journal= {arXiv preprint arXiv:1207.4026},
year = {2012}
}