On a solution to the Monge transport problem on the real line arising from the strictly concave case
Probability
2019-07-02 v1 Optimization and Control
Abstract
It is well-known that the optimal transport problem on the real line for the classical distance cost may not have a unique solution. In this paper we recover uniqueness by considering the transport problems where the costs are a power smaller than one of the distance, and letting this parameter tend to one. A complete construction of this solution that we call excursion coupling is given. This is reminiscent to the one in the convex case. It is also characterized as the solution of secondary transport problems. Moreover, a combinatoric/geometric characterization of the routes used for this transport plan is provided.
Keywords
Cite
@article{arxiv.1907.00681,
title = {On a solution to the Monge transport problem on the real line arising from the strictly concave case},
author = {Nicolas Juillet},
journal= {arXiv preprint arXiv:1907.00681},
year = {2019}
}