Computing the L1 optimal transport density: a FEM approach

The \(L^1\) optimal transport density \(\mu^*\) is the unique \(L^\infty\) solution of the Monge-Kantorovich equations. It has been recently characterized also as the unique minimizer of the \(L^1\) -transport energy functional E. In the present work we develop and we prove convergence of a numerica...

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Bibliographic Details
Published in:arXiv.org 2023-04
Main Authors: Piazzon, Federico, Facca, Enrico, Putti, Mario
Format: Article
Language:English
Subjects:
Algorithms
Density
Finite element method
Gradient flow
Mathematical analysis
Optimization
Online Access:Get full text
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Summary:The \(L^1\) optimal transport density \(\mu^*\) is the unique \(L^\infty\) solution of the Monge-Kantorovich equations. It has been recently characterized also as the unique minimizer of the \(L^1\) -transport energy functional E. In the present work we develop and we prove convergence of a numerical approxi- mation scheme for \(\mu^*\) . Our approach relies upon the combination of a FEM- inspired variational approximation of E with a minimization algorithm based on a gradient flow method.
ISSN:2331-8422