A relaxation viewpoint to Unbalanced Optimal Transport: duality, optimality and Monge formulation
Optimization and Control
2024-01-02 v1 Functional Analysis
Abstract
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.
Cite
@article{arxiv.2401.00542,
title = {A relaxation viewpoint to Unbalanced Optimal Transport: duality, optimality and Monge formulation},
author = {Giuseppe Savaré and Giacomo Enrico Sodini},
journal= {arXiv preprint arXiv:2401.00542},
year = {2024}
}
Comments
57 pages