Calculus of Variations and Geometric Measure Theory

G. Savaré - G. E. Sodini

A relaxation viewpoint to Unbalanced Optimal Transport: duality, optimality and Monge formulation

created by sodini on 02 Jan 2024



Inserted: 2 jan 2024
Last Updated: 2 jan 2024

Year: 2023

ArXiv: 2401.00542 PDF


We present a general convex relaxation approach to study a wide class of Unbalanced Optimal Transport problems for finite non-negative measures with possibly different masses. These are obtained as the lower semicontinuous and convex envelope of a cost for non-negative Dirac masses. New general primal-dual formulations, optimality conditions, and metric-topological properties are carefully studied and discussed.