This PhD focuses on the study of efficient algorithms for multimarginal and martingale constraints optimal transportation problems.
Optimal tranportation problems have various applications both in finance, in economy or in physics. In particular, we want to apply our algorithm to the computation of the Lévy-Lieb functional used in the Density Functional Theory.
However, in the case of multimarginal constraints optimal transportation problem, current algorithms scale exponentially in the number of marginal laws; which forbids the computation of the transport for large systems. We aim to have an algorithm with a linear scale using a particle algorithm.
CERMICS, École Nationale des Ponts et Chaussées
6 et 8, av. Blaise Pascal
Cité Descartes - Champs-sur-Marne
77455 Marne-la-Vallée cedex 2