Connections between optimal transport, combinatorial optimization and hydrodynamics
Brenier, Yann1
1 CNRS (CMLS, UMR7640), École Polytechnique, 91128, Palaiseau, France.
ESAIM: Mathematical Modelling and Numerical Analysis , Optimal Transport, Tome 49 (2015) no. 6, pp. 1593-1605.

We discuss a new connection between combinatorial optimization and optimal transport theory through the analysis of a variational problem coming from mathematical Fluid Mechanics. At a discrete level, this minimization problem corresponds to a quadratic assignment problem, which belongs to the NP class of combinatorial optimization. Our analysis is focused on the study of a suitable gradient flow for which we establish the global existence of dissipative solutions which are unique when smooth.

Reçu le :
DOI : 10.1051/m2an/2015034
Classification : 49, 76, 90
Mots-clés : Optimal transport, fluid mechanics, combinatorial optimization
Brenier, Yann 1

1 CNRS (CMLS, UMR7640), École Polytechnique, 91128, Palaiseau, France. 
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Brenier, Yann. Connections between optimal transport, combinatorial optimization and hydrodynamics. ESAIM: Mathematical Modelling and Numerical Analysis , Optimal Transport, Tome 49 (2015) no. 6, pp. 1593-1605. doi : 10.1051/m2an/2015034. http://www.numdam.org/articles/10.1051/m2an/2015034/

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