The Wasserstein barycenter (or centroid) problem finds a probability distribution, which represents the center of mass of N given distributions. We introduce the weak centroid problem, which replaces the Wasserstein p-distance by the weak optimal transport problem with barycentric cost. We discuss a multi-marginal version, duality and optimality for this problem.

Bio: Friedemann Krannich is currently a PhD student in Mathematics at the University of Toronto under the supervision of Prof. Robert McCann and Prof. Adrian Nachman. His research is on dynamical formulations of multi-marginal optimal transport and on weak optimal transport.