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Minimal convex extensions and finite difference discretization of the quadratic Monge-Kantorovich problem

Jean-David Benamou 1 Vincent Duval 1
1 MOKAPLAN - Méthodes numériques pour le problème de Monge-Kantorovich et Applications en sciences sociales
CEREMADE - CEntre de REcherches en MAthématiques de la DEcision, Inria de Paris
Abstract : We present an adaptation of the MA-LBR scheme to the Monge-Ampère equation with second boundary value condition, provided the target is a convex set. This yields a fast adaptive method to numerically solve the Optimal Transport problem between two absolutely continuous measures, the second of which has convex support. The proposed numerical method actually captures a specific Brenier solution which is minimal in some sense. We prove the convergence of the method as the grid stepsize vanishes and we show with numerical experiments that it is able to reproduce subtle properties of the Optimal Transport problem.
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Preprints, Working Papers, ...
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https://hal.inria.fr/hal-01616842
Contributor : Vincent Duval Connect in order to contact the contributor
Submitted on : Sunday, October 15, 2017 - 12:37:41 AM
Last modification on : Wednesday, November 17, 2021 - 12:33:14 PM
Long-term archiving on: : Tuesday, January 16, 2018 - 12:43:03 PM

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  • HAL Id : hal-01616842, version 1

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Jean-David Benamou, Vincent Duval. Minimal convex extensions and finite difference discretization of the quadratic Monge-Kantorovich problem. 2017. ⟨hal-01616842v1⟩

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