Summer school 2019
A NUMERICAL INTRODUCTION
TO OPTIMAL TRANSPORT
Inria, 2 Rue Simone Iff, 75012 Paris, Paris,
May 13 to May 17, 2019.
Summer schools are intended for researchers, engineers and PhD students.
It offers a detailed presentation of the state of the art of the proposed scientific computing topic and is complemented by numerical tutorials.
Context : Optimal Mass Transportation is a mathematical research topic which started two centuries ago with Monge’s work on the “Théorie des déblais et des remblais” This engineering problem consists in minimizing the transport cost between two given mass densities. In the 40’s, Kantorovich introduced a powerful linear relaxation and introduced its dual formulation. The Monge-Kantorovich problem became a specialized research topic in optimization and Kantorovich obtained the 1975 Nobel prize in economics for his contributions to resource allocations problems. Since the seminal discoveries of Brenier in the 90’s, Optimal Transportation has received renewed attention from mathematical analysts with two recent fields Medal awarded Villani (2010) and Figalli (2018). Optimal Mass Transportation is today a mature area of mathematical analysis with a constantly growing range of applications. Optimal Transportation and the associated Wassertein distance for densities has also received a lot of attention from probabilists. The research and development of numerical methods for Optimal Transportation and Op- timal Transportation related problems has gained significant momentum in the last 5 years and several class of methods have been or are currently applied in diverse applications fields : astropysics, satellite data analysis, freeform optics, academic fluid models, crowd motion … Three new books by F. Santambrogio ( “Optimal Transportation for applied mathematicans” ), A. Galichon (“Optimal Transport in Economics”) and Peyré / Cuturi (“ Computational Optimal Transport”) have been published since 2015.