Numerical solution of the Monge-Kantorovich problem by Picard iterations

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

1 IMB - Institut de Mathématiques de Bordeaux
2 MC2 - Modélisation, contrôle et calcul

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.

Mots clés: Optimal transport; Monge-Kantorovich problem; Numerical methods; Picard iterations

Domaines: Analyse numérique [math.NA]

Afaf Bouharguane, Angelo Iollo, Lisl Weynans. Numerical solution of the Monge-Kantorovich problem by Picard iterations. [Research Report] RR-8477, INRIA. 2014. ⟨hal-00946252⟩