A simple procedure to map two probability measures in Rᵈ is the so-called Knothe–Rosenblatt rearrangement, which consists of 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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Carlier et al. (2010) studied this question.
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