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On Convergence of Capacity-Constrained Optimal Transport

Student: Emelchenkov Anton

Supervisor: Alexander Kolesnikov

Faculty: Faculty of Mathematics

Educational Programme: Mathematics (Bachelor)

Year of Graduation: 2020

In 2012 J. Korman and R. J. McCann introduced capacity-constrained optimal transport. In this paper we study two types of capacity constraints, conditional and relative. For both cases we introduce a transportation cost based on the Kantorovich distance. We prove that these functionals Gamma-converge to the Kantorovich cost for unconstrained problem. Furthermore, we prove pointwise convergence for the case of relative constraint. In addition, we estimate the lower bound for both costs and give an estimate of difference between costs of two given plans, one of which is an optimal map.

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