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From Knothes transport to Breniers map and a continuation method for optimal transport

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 نشر من قبل Alfred Galichon
 تاريخ النشر 2008
  مجال البحث
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A simple procedure to map two probability measures in $mathbb{R}^d$ is the so-called emph{Knothe-Rosenblatt rearrangement}, which consists in rearranging monotonically the marginal distributions of the last coordinate, and then the conditional distributions, iteratively. We show that this mapping is the limit of solutions to a class of Monge-Kantorovich mass transportation problems with quadratic costs, with the weights of the coordinates asymptotically dominating one another. This enables us to design a continuation method for numerically solving the optimal transport problem.



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