The entropic regularization of the Monge problem on the real line

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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Submitted on : Thursday, August 16, 2018 - 1:44:30 AM
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Simone Di Marino, Jean Louet. The entropic regularization of the Monge problem on the real line. SIAM Journal on Mathematical Analysis, Society for Industrial and Applied Mathematics, In press, 50 (4), pp.3451 - 3477. ⟨10.1137/17M1123523⟩. ⟨hal-01498732v4⟩

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