A relaxation viewpoint to unbalanced optimal transport: duality, optimality and Monge formulation. (English. French summary) Zbl 07882131
Authors’ 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.
Reviewer: Stepan Agop Tersian (Rousse)
MSC:
| 49Q22 | Optimal transportation |
| 49J45 | Methods involving semicontinuity and convergence; relaxation |
| 28A33 | Spaces of measures, convergence of measures |
| 49K27 | Optimality conditions for problems in abstract spaces |
Keywords:
unbalanced optimal transport; Monge and Kantorovich problems; duality; Gaussian Hellinger-Kantorovich metric; optimality conditionsSoftware:
EMDReferences:
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