Geodesic
Multi-marginal optimal transport: Theory and applications
Pass, Brendan1
1 Department of Mathematical and Statistical Sciences, 632 CAB, University of Alberta, Edmonton, Alberta, T6G 2G1, Canada.
ESAIM: Mathematical Modelling and Numerical Analysis , Optimal Transport, Tome 49 (2015) no. 6, pp. 1771-1790 Cet article a éte moissonné depuis la source Numdam

Voir la notice de l'article

Over the past five years, multi-marginal optimal transport, a generalization of the well known optimal transport problem of Monge and Kantorovich, has begun to attract considerable attention, due in part to a wide variety of emerging applications. Here, we survey this problem, addressing fundamental theoretical questions including the uniqueness and structure of solutions. The answers to these questions uncover a surprising divergence from the classical two marginal setting, and reflect a delicate dependence on the cost function, which we then illustrate with a series of examples. We go on to describe some applications of the multi-marginal optimal transport problem, focusing primarily on matching in economics and density functional theory in physics.

Reçu le :
DOI : 10.1051/m2an/2015020
Classification : 49K30, 49J30, 49K20, 91B68, 81V45, 90C05, 35J96
Keywords: Multi-marginal optimal transport, Monge−Kantorovich problem, structure of solutions, uniqueness of solutions, matching, purity, density functional theory, strictly correlated electrons

Pass, Brendan 1

1 Department of Mathematical and Statistical Sciences, 632 CAB, University of Alberta, Edmonton, Alberta, T6G 2G1, Canada. 
@article{M2AN_2015__49_6_1771_0,
     author = {Pass, Brendan},
     title = {Multi-marginal optimal transport: {Theory} and applications},
     journal = {ESAIM: Mathematical Modelling and Numerical Analysis },
     pages = {1771--1790},
     year = {2015},
     publisher = {EDP-Sciences},
     volume = {49},
     number = {6},
     doi = {10.1051/m2an/2015020},
     mrnumber = {3423275},
     zbl = {1330.49050},
     language = {en},
     url = {http://geodesic.mathdoc.fr/articles/10.1051/m2an/2015020/}
}
TY  - JOUR
AU  - Pass, Brendan
TI  - Multi-marginal optimal transport: Theory and applications
JO  - ESAIM: Mathematical Modelling and Numerical Analysis 
PY  - 2015
SP  - 1771
EP  - 1790
VL  - 49
IS  - 6
PB  - EDP-Sciences
UR  - http://geodesic.mathdoc.fr/articles/10.1051/m2an/2015020/
DO  - 10.1051/m2an/2015020
LA  - en
ID  - M2AN_2015__49_6_1771_0
ER  - 
%0 Journal Article
%A Pass, Brendan
%T Multi-marginal optimal transport: Theory and applications
%J ESAIM: Mathematical Modelling and Numerical Analysis 
%D 2015
%P 1771-1790
%V 49
%N 6
%I EDP-Sciences
%U http://geodesic.mathdoc.fr/articles/10.1051/m2an/2015020/
%R 10.1051/m2an/2015020
%G en
%F M2AN_2015__49_6_1771_0
Pass, Brendan. Multi-marginal optimal transport: Theory and applications. ESAIM: Mathematical Modelling and Numerical Analysis , Optimal Transport, Tome 49 (2015) no. 6, pp. 1771-1790. doi: 10.1051/m2an/2015020

Cité par Sources :