Calculus of Variations and Geometric Measure Theory
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S. Di Marino - J. Louet

The entropic regularization of the Monge problem on the real line

created by louet on 30 Mar 2017
modified on 30 Jan 2018

[BibTeX]

Accepted Paper

Inserted: 30 mar 2017
Last Updated: 30 jan 2018

Journal: SIAM J. Math. Anal.
Year: 2018

ArXiv: 1703.10457 PDF

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.

Keywords: Monge problem, Optimal transport, $\Gamma$-convergence, Monotone transport, Entropic regularization


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