Advances in Numerical Optimal Transportation (15w5067)
Jean-David Benamou (INRIA Rocquencourt )
Yann Brenier (CNRS, Ecole Polytechnique)
Adam Oberman (McGill University)
Optimal Transportation (OT) is now a mature field of mathematical analysis. It is rapidly expanding as a modelization tool (Economics, Electomagnetics, Inverse problems in general, Image Processing ... ...). Research on numerical solvers and methods is unfortunately still underdeveloped and we face two important challenges :
- Develop performant multi-purpose solvers for the "classical" Monge-Kantorovitch problem (the 2-Wasserstein distance computation). - Develop method and solvers for a large number of non trivial extensions of the notion the Monge-Kantorovitch problem : multi-marginal OT, C-Convex ground costs, OT of vector fields ... which are important in view of potential applications.
The Goal of the proposed workshop is - To gather numerical analysts active in this field in order to get a clearer picture of the state of the art of numerical OT. - Mix these people with the best specialist of OT analysis in order to discuss the (sometime technical) mathematics of the extensions mentioned in B).