Numerical resolution of an “unbalanced” mass transport problem

Jean-David Benamou

ESAIM: Mathematical Modelling and Numerical Analysis (2010)

  • Volume: 37, Issue: 5, page 851-868
  • ISSN: 0764-583X

Abstract

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We introduce a modification of the Monge–Kantorovitch problem of exponent 2 which accommodates non balanced initial and final densities. The augmented Lagrangian numerical method introduced in [6] is adapted to this “unbalanced” problem. We illustrate the usability of this method on an idealized error estimation problem in meteorology.

How to cite

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Benamou, Jean-David. "Numerical resolution of an “unbalanced” mass transport problem." ESAIM: Mathematical Modelling and Numerical Analysis 37.5 (2010): 851-868. <http://eudml.org/doc/194194>.

@article{Benamou2010,
abstract = { We introduce a modification of the Monge–Kantorovitch problem of exponent 2 which accommodates non balanced initial and final densities. The augmented Lagrangian numerical method introduced in [6] is adapted to this “unbalanced” problem. We illustrate the usability of this method on an idealized error estimation problem in meteorology. },
author = {Benamou, Jean-David},
journal = {ESAIM: Mathematical Modelling and Numerical Analysis},
keywords = {Monge–Kantorovitch problem; Wasserstein distance; augmented Lagrangian method.; penalization technique; Monge-Kantorovitch problem; augmented Lagrangian numerical method; error estimation; meteorology},
language = {eng},
month = {3},
number = {5},
pages = {851-868},
publisher = {EDP Sciences},
title = {Numerical resolution of an “unbalanced” mass transport problem},
url = {http://eudml.org/doc/194194},
volume = {37},
year = {2010},
}

TY - JOUR
AU - Benamou, Jean-David
TI - Numerical resolution of an “unbalanced” mass transport problem
JO - ESAIM: Mathematical Modelling and Numerical Analysis
DA - 2010/3//
PB - EDP Sciences
VL - 37
IS - 5
SP - 851
EP - 868
AB - We introduce a modification of the Monge–Kantorovitch problem of exponent 2 which accommodates non balanced initial and final densities. The augmented Lagrangian numerical method introduced in [6] is adapted to this “unbalanced” problem. We illustrate the usability of this method on an idealized error estimation problem in meteorology.
LA - eng
KW - Monge–Kantorovitch problem; Wasserstein distance; augmented Lagrangian method.; penalization technique; Monge-Kantorovitch problem; augmented Lagrangian numerical method; error estimation; meteorology
UR - http://eudml.org/doc/194194
ER -

References

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