Topological Optimization and Optimal Transport

Part II

Preface

Optimal Transportation is now a widely studied topic, due to its numerous connections with many mathematical theories and domains of applied mathematics. If the renewed interest by mathematicians for this topic dates back to the works by Brenier in the late 1980s, we can probably say that such an interest has mainly been theoretical (existence and regularity of the solutions, applications to functional and geometrical inequalities, connections with differential geometry and curvature conditions, extensions to abstract metric spaces...) for more than twenty years. An international community working on the applications of optimal transport (in image processing, in PDE modeling physical or biological phenomena, in economics...) ...