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arXiv · 2404.00003

Algorithms for constrained optimal transport

Martin Corless·Anthony Quinn·Sarah Boufelja·Robert Shorten
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Abstract

We derive iterative scaling algorithms of the Sinkhorn-Knopp (SK) type for constrained optimal transport. The constraints are in the form of prior-imposed zeroes in the transport plan. Based on classical Bregman arguments, we prove asymptotic convergence of our algorithms to a unique optimal solution. New insights obtained from the convergence proof are highlighted. An example from electrical vehicle charging in a smart city context is outlined, in which the prior zero-constraints prevent energy from being transported from some providers to some vehicles.

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Martin Corless, Anthony Quinn, Sarah Boufelja, Robert Shorten. 2024-02-16. Algorithms for constrained optimal transport. https://arxiv.org/abs/2404.00003

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