Regularity of unbalanced optimal transport
speaker: Roberta Ghezzi (Università di Roma Tor Vergata)abstract: Recently, optimal transport has been extended to measures of positive and finite mass (on the Euclidean space or on a Riemannian manifold) CSPV16, CPSV18, KMV16, LMS18, giving rise to the so-called unbalanced optimal transport. On the set of positive Radon measures on a metric space, the Wasserstein- Fisher-Rao distance is a natural generalization of the classical Wasserstein distance and admits different equivalent formulations (dynamical, semi-coupling, dual, Kantorovich formulations). In a joint work with F.-X. Vialard and T. Gallou ̈et we show how to reduce regularity of unbalanced optimal transport to regularity of a standard optimal transport problem and we prove that unbalanced optimal transport is regular on spheres by computing the Ma-Trudinger-Wang tensor. CPSV18 L. Chizat, G. Peyre, B. Schmitzer, and F.- X. Vialard. Unbalanced optimal transport: dynamic and Kantorovich formulations. J. Funct. Anal., 274(11):3090–3123, 2018. CSPV16 L. Chizat, B. Schmitzer, G. Peyr ́e, and F.-X. Vialard. An Interpolating Distance between Optimal Transport and Fisher-Rao. Found. Comp. Math., 2016. KMV16 S. Kondratyev, L. Monsaingeon, and D. Vorotnikov. A new optimal trasnport distance on the space of finite Radon measures. Adv. Differential Equations, 21(11):1117–1164, 2016. LMS18 M. Liero, A. Mielke, and G. Savar ́e. Optimal Entropy-Transport problems and a new Hellinger-Kantorovich distance between positive measures. Inventiones Math., 2018.
timetable:
Tue 9 May, 16:30 - 17:00, Aula Dini
<< Go back