Jordan–Kinderlehrer–Otto scheme

Summary

The Jordan–Kinderlehrer–Otto scheme, or JKO scheme, is a time discretization of a gradient flow in the space of probability measures with the Wasserstein distance. At each step it minimizes the energy plus a penalty for moving far, in Wasserstein distance, from the previous measure. Richard Jordan, David Kinderlehrer and Felix Otto introduced it in 1998 and proved that it converges to solutions of the Fokker–Planck equation. It showed that the heat equation is the gradient flow of the entropy for the Wasserstein distance, and started the theory of Wasserstein gradient flows.