Jun Kitagawa : A convergent Newton algorithm for semi-discrete optimal transport

The optimal transport (Monge-Kantorovich) problem is a variational problem involving transportation of mass subject to minimizing some kind of energy, and it arises in connection with many parts of math, both pure and applied. In this talk, I will discuss a numerical algorithm to approximate solutions in the semi-discrete case. We propose a damped Newton algorithm which exploits the structure of the associated dual problem, and using geometric implications of the regularity theory of Monge-Amp{\`e}re equations, we are able to rigorously prove global linear convergence and local superlinear convergence of the algorithm. This talk is based on joint work with Quentin M{\’e}rigot and Boris Thibert.

• Category: Applied Math and Analysis
• Duration: 01:34:47
• Date:  March 3, 2020 at 3:10 PM
• Tags:   seminar, Applied Math And Analysis Seminar