Numerical solution of the Monge–Kantorovich problem by density lift-up continuation

Afaf Bouharguane (1, 2) , Angelo Iollo (2, 1) , Lisl Weynans (2, 1)

1 MEMPHIS - Modeling Enablers for Multi-PHysics and InteractionS
2 IMB - Institut de Mathématiques de Bordeaux

We present an iterative method to numerically solve the L² Monge-Kantorovich problem. The method is based on a Picard fixed point iteration of the linearized problem. Examples relative to the transport of two-dimensional densities show that the present method can significantly reduce the computational time over existing methods, especially when the Wasserstein distance between the densities is small.

Domaines: Analyse numérique [math.NA]

Afaf Bouharguane, Angelo Iollo, Lisl Weynans. Numerical solution of the Monge–Kantorovich problem by density lift-up continuation. ESAIM: Mathematical Modelling and Numerical Analysis, 2015, Special Issue - Optimal Transport, 49 (6), pp.1577 ⟨10.1051/m2an/2015024⟩. ⟨hal-01250636⟩