A least-squares method for optimal transport using the Monge-Ampère equation

C.R. Prins; J.H.M. Thije Boonkkamp, ten; W.L. IJzerman; T.W. Tukker

doi:10.1137/140986414

A least-squares method for optimal transport using the Monge-Ampère equation

C.R. Prins, J.H.M. Thije Boonkkamp, ten, W.L. IJzerman, T.W. Tukker

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Abstract

In this article we introduce a novel numerical method to solve the problem of optimal transport and the related elliptic Monge--Ampère equation. It is one of the few numerical algorithms capable of solving this problem efficiently with the proper transport boundary condition. The computation time scales well with the grid size and has the additional advantage that the target domain may be nonconvex. We present the method and several numerical experiments.

Original language	English
Pages (from-to)	B937-B961
Journal	SIAM Journal on Scientific Computing
Volume	37
Issue number	6
DOIs	https://doi.org/10.1137/140986414
Publication status	Published - 2015

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title = "A least-squares method for optimal transport using the Monge-Amp{\`e}re equation",

abstract = "In this article we introduce a novel numerical method to solve the problem of optimal transport and the related elliptic Monge--Amp{\`e}re equation. It is one of the few numerical algorithms capable of solving this problem efficiently with the proper transport boundary condition. The computation time scales well with the grid size and has the additional advantage that the target domain may be nonconvex. We present the method and several numerical experiments.",

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AU - Tukker, T.W.

PY - 2015

Y1 - 2015

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AB - In this article we introduce a novel numerical method to solve the problem of optimal transport and the related elliptic Monge--Ampère equation. It is one of the few numerical algorithms capable of solving this problem efficiently with the proper transport boundary condition. The computation time scales well with the grid size and has the additional advantage that the target domain may be nonconvex. We present the method and several numerical experiments.

U2 - 10.1137/140986414

DO - 10.1137/140986414

M3 - Article

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SP - B937-B961

JO - SIAM Journal on Scientific Computing

JF - SIAM Journal on Scientific Computing

IS - 6

ER -

A least-squares method for optimal transport using the Monge-Ampère equation

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