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 nonpenalized problem, the most "diffuse" one on the zones where it may have a density.
The entropic regularization of the monge problem on the real line
Di Marino S.;
2018-01-01
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 nonpenalized problem, the most "diffuse" one on the zones where it may have a density.
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