Dynamic Formulation of Optimal Transportation and Variational Relaxation of Euler Equations
We will briefly recall the classical Optimal Transportation Framework and its Dynamic relaxations. We will show the link between these Dynamic formulation and the so-called Multi-Marginal extension of Optimal Transportation. We will then describe the so-called Iterative Proportional Fitting Procedure (IPFP aka Sinkhorn method) which can be efficiently applied to the multi-marginal OT setting. Finally we will show how this can be used to compute generalized Euler geodesics due to Brenier. This problem can be considered as the oldest instance of Multi-Marginal Optimal Transportation problem.
Joint work with Guillaume Carlier and Luca Nenna (Ceremade, Paris Dauphine and Mokaplan INRIA).
Presentation by: Jean-David Benamou. INRIA, France.