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arXiv · 2401.00542

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

Giuseppe Savaré·Giacomo Enrico Sodini
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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.

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Giuseppe Savaré, Giacomo Enrico Sodini. 2023-12-31. A relaxation viewpoint to Unbalanced Optimal Transport: duality, optimality and Monge formulation. https://arxiv.org/abs/2401.00542

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