The Sinkhorn algorithm, parabolic optimal transport and geometric Monge–Ampère equations
The Sinkhorn algorithm, parabolic optimal transport and geometric Monge–Ampère equations
Abstract We show that the discrete Sinkhorn algorithm—as applied in the setting of Optimal Transport on a compact manifold—converges to the solution of a fully non-linear parabolic PDE of Monge–Ampère type, in a large-scale limit. The latter evolution equation has previously appeared in different contexts (e.g. on the torus it …