Section: Overall Objectives

Highlights of the Year

The paper [6] resolves numerically the Monge-Ampère formulation of the Optimal Tansportation problem with quadratic cost with the correct “second boundary value” boundary conditions. It is worth pointing that this has been an open problem for a while. The same paper proposes a fast and robust Newton method (empirically linear) which can be applied to degenerate cases. This potentially means progress in many applications of Optimal Mass Transportation. The method has, for instance, been reimplemented in [72] by TU Eindhoven researchers in collaboration with Philips Lightning Labs to simulate the design of reflectors. In 2013, the method was the topic of invited presentations at the Collège de France applied math seminar, at MSRI (UC Berkeley) special program on Optimal Mass Transportation and at SIAM annual conference on PDE analysis.

Figure 1. Top : the color map of the mass to be transported to a constant mass density ellipse, dark blue is no mass - Bottom : the deformation under the optimal transportation map of the initial computational cartesian grid on the top square.