  In this paper, we present a numerical method, based on iterative Bregman
projections, to solve the optimal transport problem with Coulomb cost. This is
related to the strong interaction limit of Density Functional Theory. The first
idea is to introduce an entropic regularization of the Kantorovich formulation
of the Optimal Transport problem. The regularized problem then corresponds to
the projection of a vector on the intersection of the constraints with respect
to the Kullback-Leibler distance. Iterative Bregman projections on each
marginal constraint are explicit which enables us to approximate the optimal
transport plan. We validate the numerical method against analytical test cases.
