Mass transportation with LQ cost functions
Optimization and Control
2011-05-23 v1 Systems and Control
Abstract
We study the optimal transport problem in the Euclidean space where the cost function is given by the value function associated with a Linear Quadratic minimization problem. Under appropriate assumptions, we generalize Brenier's Theorem proving existence and uniqueness of an optimal transport map. In the controllable case, we show that the optimal transport map has to be the gradient of a convex function up to a linear change of coordinates. We give regularity results and also investigate the non-controllable case.
Cite
@article{arxiv.1105.4037,
title = {Mass transportation with LQ cost functions},
author = {Ahed Hindawi and Ludovic Rifford and Jean-Baptiste Pomet},
journal= {arXiv preprint arXiv:1105.4037},
year = {2011}
}