On entropy-transport problems and the Hellinger--Kantorovich distance
Séminaire Modèles et Algorithmes Déterministes: EDP-MOISE-MGMI
26/01/2017 - 11:00 Mr Matthias Liero (WIAS, Berlin) Salle 106 - Batiment IMAG
In this talk, we will present a general class of variational problems involving entropy-transport minimization with respect to a couple of given finite measures with possibly unequal total mass. These optimal entropy-transport problems can be regarded as a natural generalization of classical optimal transportation problems. With an appropriate choice of the entropy/cost functionals they provide a distance between measures that exhibits interesting geometric features. We call this distance Hellinger-Kantorovich distance as it can be seen as an interpolation between the Hellinger and the Kantorovich-Wasserstein distance. The link to the entropy- transport minimization problems relies on convex duality in a surprising way. Moreover, a dynamic Benamou-Brenier characterization also shows the role of these distances in dynamic processes involving creation or annihilation of masses. Finally, we will give a characterization of geodesic curves and of convex functionals. It is a joint work with Giuseppe Savaré and Alexander Mielke.