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On Fluid mechanics formulation of Monge-Kantorovich Mass Transfer Problem

Kazufumi Ito
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Abstract

The Monge-Kantorovich mass transfer problem is equivalently formulated as a convex optimization problem for a potential function. In the light of this formulation an interative algorithm is developed for determining the solution. It is a gradient flow algorithm and each iterate solves a linear elliptic equation. Well-posedness and convergence of the proposed method are analyzed and numerical findings are presented.

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Kazufumi Ito. 2007-02-08. On Fluid mechanics formulation of Monge-Kantorovich Mass Transfer Problem. https://arxiv.org/abs/math/0702235

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