Numerical resolution of an “unbalanced” mass transport problem
ESAIM: Mathematical Modelling and Numerical Analysis , Tome 37 (2003) no. 5, pp. 851-868.

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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.

DOI : 10.1051/m2an:2003058
Classification : 35J60, 65K10, 78A05, 90B99
Mots-clés : Monge-Kantorovitch problem, Wasserstein distance, augmented lagrangian method 
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     title = {Numerical resolution of an {\textquotedblleft}unbalanced{\textquotedblright} mass transport problem},
     journal = {ESAIM: Mathematical Modelling and Numerical Analysis },
     pages = {851--868},
     publisher = {EDP-Sciences},
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Benamou, Jean-David. Numerical resolution of an “unbalanced” mass transport problem. ESAIM: Mathematical Modelling and Numerical Analysis , Tome 37 (2003) no. 5, pp. 851-868. doi : 10.1051/m2an:2003058. https://geodesic-test.mathdoc.fr/articles/10.1051/m2an:2003058/

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