Kantorovich Initiative Seminar: Andrea Natale

In this talk, we study a variational problem that provides a way to extend minimizing geodesics connecting two given probability measures in the Wasserstein space for all times. This is achieved by allowing negative coefficients in the classical variational characterization of Wasserstein barycenters. Using Toland duality, we show that this problem is equivalent to a specific type of Wasserstein projection onto the set of measures dominated in the convex order by a given measure. We propose a computational approach to solve the problem, exploiting an explicit characterization of the convex set of discrete measures dominated in the convex order by an absolutely continuous measure. Finally, we give a concrete application of this in materials science, of fitting a Laguerre tessellation to an electron backscatter diffraction (EBSD) image of a steel.