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arXiv · 1703.10457

The entropic regularization of the Monge problem on the real line

Simone Di Marino·Jean Louet
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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.

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Simone Di Marino, Jean Louet. 2018-08-16. The entropic regularization of the Monge problem on the real line. https://doi.org/10.1137/17m1123523

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