@Article{JCM-38-933,
author = {Oberman , Adam M. and Ruan , Yuanlong},
title = {Solution of Optimal Transportation Problems Using a Multigrid Linear Programming Approach},
journal = {Journal of Computational Mathematics},
year = {2020},
volume = {38},
number = {6},
pages = {933--951},
abstract = {<p style="text-align: justify;">We compute and visualize solutions to the Optimal Transportation (OT) problem for
a wide class of cost functions. The standard linear programming (LP) discretization of
the continuous problem becomes intractable for moderate grid sizes. A grid refinement
method results in a linear cost algorithm. Weak convergence of solutions is established and
barycentric projection of transference plans is used to improve the accuracy of solutions.
Optimal maps between nonconvex domains, partial OT free boundaries, and high accuracy
barycenters are presented.</p>},
issn = {1991-7139},
doi = {https://doi.org/10.4208/jcm.1907-m2017-0224},
url = {http://global-sci.org/intro/article_detail/jcm/16974.html}
}