Geodesic
Numerical solution of the Monge–Kantorovich problem by density lift-up continuation
Bouharguane, Afaf1  ; Iollo, Angelo1  ; Weynans, Lisl1 
1 Institut de Mathématiques de Bordeaux, UMR 5251 CNRS, Université de Bordeaux and Equipe-projet MEMPHIS, Inria Bordeaux Sud-Ouest, 33405 Talence, France.
ESAIM: Mathematical Modelling and Numerical Analysis , Optimal Transport, Tome 49 (2015) no. 6, pp. 1577-1592

Voir la notice de l'article provenant de la source Numdam

We present an numerical method to solve the L 2 Monge–Kantorovich problem. The method is based on a continuation approach where we iteratively solve the linearized mass conservation equation, progressively decreasing a constant lift-up to map compact support densities in the limit. A Lagrangian as well as an Eulerian integration scheme are proposed. Several examples relative to the transport of two-dimensional densities are investigated, showing that the present methods can significantly reduce the computational effort.

Reçu le :
DOI : 10.1051/m2an/2015024
Classification : 68U01, 65K05
Keywords: Optimal transport, Monge–Kantorovich problem, numerical solution, Newton method, continuation approach

Bouharguane, Afaf 1 ; Iollo, Angelo 1 ; Weynans, Lisl 1

1 Institut de Mathématiques de Bordeaux, UMR 5251 CNRS, Université de Bordeaux and Equipe-projet MEMPHIS, Inria Bordeaux Sud-Ouest, 33405 Talence, France. 
@article{M2AN_2015__49_6_1577_0,
     author = {Bouharguane, Afaf and Iollo, Angelo and Weynans, Lisl},
     title = {Numerical solution of the {Monge{\textendash}Kantorovich} problem by density lift-up continuation},
     journal = {ESAIM: Mathematical Modelling and Numerical Analysis },
     pages = {1577--1592},
     publisher = {EDP-Sciences},
     volume = {49},
     number = {6},
     year = {2015},
     doi = {10.1051/m2an/2015024},
     mrnumber = {3423265},
     zbl = {1348.65098},
     language = {en},
     url = {http://geodesic.mathdoc.fr/articles/10.1051/m2an/2015024/}
}
TY  - JOUR
AU  - Bouharguane, Afaf
AU  - Iollo, Angelo
AU  - Weynans, Lisl
TI  - Numerical solution of the Monge–Kantorovich problem by density lift-up continuation
JO  - ESAIM: Mathematical Modelling and Numerical Analysis 
PY  - 2015
SP  - 1577
EP  - 1592
VL  - 49
IS  - 6
PB  - EDP-Sciences
UR  - http://geodesic.mathdoc.fr/articles/10.1051/m2an/2015024/
DO  - 10.1051/m2an/2015024
LA  - en
ID  - M2AN_2015__49_6_1577_0
ER  - 
%0 Journal Article
%A Bouharguane, Afaf
%A Iollo, Angelo
%A Weynans, Lisl
%T Numerical solution of the Monge–Kantorovich problem by density lift-up continuation
%J ESAIM: Mathematical Modelling and Numerical Analysis 
%D 2015
%P 1577-1592
%V 49
%N 6
%I EDP-Sciences
%U http://geodesic.mathdoc.fr/articles/10.1051/m2an/2015024/
%R 10.1051/m2an/2015024
%G en
%F M2AN_2015__49_6_1577_0
Bouharguane, Afaf; Iollo, Angelo; Weynans, Lisl. Numerical solution of the Monge–Kantorovich problem by density lift-up continuation. ESAIM: Mathematical Modelling and Numerical Analysis , Optimal Transport, Tome 49 (2015) no. 6, pp. 1577-1592. doi: 10.1051/m2an/2015024

Cité par Sources :