Unbalanced Optimal Transport: Convex Relaxation and Dynamic Perspectives

Speaker: Giuseppe Savare

Date: Thu, Nov 30, 2023

Location: PIMS, University of Washington, Zoom, Online

Conference: Kantorovich Initiative Seminar

Subject: Mathematics

Class: Scientific

CRG: Pacific Interdisciplinary Hub on Optimal Transport


I will try to present an overview of some results of unbalanced optimal transport for positive measures with different total masses, showing the crucial role of the so-called cone representation and of the corresponding homogeneous marginals. The cone perspective naturally arises in the convex-relaxation approach to optimal transport; in the more specific case of the Hellinger-Kantorovich (aka Fisher-Rao) metric, it provides a natural tool for representing solutions of the dual dynamical formulation via Hamilton-Jacobi equations, and it is very useful for studying the geodesic convexity of entropy type functionals. (In collaboration with M. Liero, A. Mielke, G. Sodini)

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