A Short Course on Optimal Transportation Problem
Professor Toshio MikamiHiroshima University 上午 10:00–12:00 鴻經館 107 室Abstract:
In this lecture, we briefly introduce the Monge-Kantorovich Problem and the Knothe-Rosenblatt rearrangement as an application. If time permitted, we also discuss the stochastic control analogue.
The lectures will cover the following.
Chapter 1. Monge-Kantorovich Problem
1 Monge's problem
2 Kantorovich's problem
3 Duality Theorem
4 Solution to Kantorovich's problem
5 A simple proof of Duality Theorem
6 One-dimensional case
Chapter 2. Knothe-Rosenblatt rearrangement
7 Knothe-Rosenblatt rearrangement
8 Brunn-Minkowskii's inequality