Notes on optimal transportation
This article provides a detailed introduction to the mathematical theory of optimal transportation. Based on a series of university lecture notes, it provides a useful insight in this area of optimization. The article begins with a section providing the necessary historic background of the problem. This is followed by a presentation of the general discrete optimal transportation problem and its link to the adverse selection problem, including important elements of \(u\)-convex analysis. Several theorems are presented in this section, with detailed proofs. In the fourth section, the article proceeds to study the continuous case, where the existence of a solution is non-trivial, focussing on Brenier's theorems. The article concludes with an outline of unsolved problems in the area and a list of relevant references.
scientific article; zbMATH DE number 5673335