Optimal transportation with capacity constraints
By Jonathan Korman, Robert J. McCann. 2012
53 citations recorded by the source corpus.
The classical problem of optimal transportation can be formulated as a linear optimization problem on a convex domain: among all joint measures with fixed marginals find the optimal one, where optimality is measured against a cost function. Here we consider a natural but largely unexplored variant of this problem by imposing a pointwise constraint on the joint (absolutely continuous) measures: among all joint densities with fixed marginals and which are dominated by a given density, find the optimal one. For this variant, we show local non-degeneracy of the cost function implies every minimizer is extremal in the convex set of competitors, hence unique. An appendix develops rudiments of a duality theory for this problem, which allows us to compute several suggestive examples.
Subfields: Applied Mathematics, Statistics and Probability
View Paper: https://www.semanticscholar.org/paper/7cf8a31aa8877261021f937e67aecea0ce1ebcfa
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In Applied Mathematics
- G. Peyr'e
- Marco Cuturi
- Jean-David Benamou
- Guillaume Carlier
- Filippo Santambrogio
- Martin Jaggi
- Sidak Pal Singh
- Victor M. Panaretos
In Statistics and Probability
Citations in the corpus
- Computational Optimal Transport (2018, background): “The optimal transport with capacity constraint [Korman and McCann, 2015] corresponds to imposing that the density ρπ (for instance, with respect to the Lebesgue measure) is upper bounded C = {π : ρπ ≤ κ} (10.”
- Iterative Bregman Projections for Regularized Transportation Problems (2014, background): “2 Capacity Constrained Transport Korman and McCann proposed and studied in [38, 39] a variant of the classical OT problem when there is an upper bound on the coupling weights so as to capture transport capacity constraints.”