On some Newton methods and their convergence for semidiscrete optimal transport

In this talk I will discuss some numerical methods for the semidiscrete optimal transport (also Monge-Kantorovich) problem, and a variant with storage fees. In this problem, one desires to transport an absolutely continuous measure to a discrete one, subject to minimizing some associated energy. As it turns out, convergence properties of such algorithms are closely related to the geometric properties of the associated minimizing transport.

This talk is based on joint work with Q. Mérigot and B. Thibert, and M. Bansil.