Map-compatible decomposition of transport paths
Analysis of PDEs
2023-10-09 v1 Optimization and Control
Abstract
In the Monge-Kantorovich transport problem, the transport cost is expressed in terms of transport maps or transport plans, which play crucial roles there. A variant of the Monge-Kantorovich problem is the ramified (branching) transport problem that models branching transport systems via transport paths. In this article, we showed that any cycle-free transport path between two atomic measures can be decomposed into the sum of a map-compatible path and a plan-compatible path. Moreover, we showed that each stair-shaped transport path can be decomposed into the difference of two map-compatible transport paths.
Keywords
Cite
@article{arxiv.2310.03825,
title = {Map-compatible decomposition of transport paths},
author = {Qinglan Xia and Haotian Sun},
journal= {arXiv preprint arXiv:2310.03825},
year = {2023}
}