Monge-Kantorovich Optimal Transport
Organizers
Speaker
Time
Tuesday, December 30, 2025 3:15 PM - 4:15 PM
Venue
A3-1-101
Online
Zoom 482 240 1589
(BIMSA)
Abstract
We begin by a brief overview of both the Monge and Kantorovich problems of optimal transport. We show that support of the optimal Kantorovich plan is $c$-cyclically monotone, which reduces to monotonicity in a special case. This then shows that the support of the Kantorovich plan is contained in the graph of the subdifferential of a convex function. The Brenier theorem then shows that the gradient of a convex function can be used as the optimal pushforward map of the Monge problem in the case where the source measure is absolutely continuous with respect to Lebesgue, which shows that the Kantorovich plan is concentrated on a set of Lebesgue measures zero. The key part will introduce entropy regularization.