# The entropic regularization of the Monge problem on the real line

created by louet on 30 Mar 2017

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Submitted Paper

Inserted: 30 mar 2017
Last Updated: 30 mar 2017

Year: 2017

Abstract:

We study the entropic regularization of the optimal transport problem in dimension 1 when the cost function is the distance $c(x,y)= y-x$. The selected plan at the limit is, among those which are optimal for the non-penalized problem, the most "diffuse" one on the zones where it may have a density.