Insights into capacity constrained optimal transport
arXiv:1304.6456 · doi:10.1073/pnas.1221333110
Abstract
A variant of the classical optimal transportation problem is: among all joint measures with fixed marginals and which are dominated by a given density, find the optimal one. Existence and uniqueness of solutions to this variant were established in \cite{KM11}. In the present manuscript, we expose an unexpected symmetry leading to the first explicit examples in two and more dimensions. These are inspired in part by simulations in one dimension which display singularities and topology and in part by two further developments: the identification of all extreme points in the feasible set, and a new approach to uniqueness based on constructing feasible perturbations.
11 pages, 3 figures
References in corpus (1)
Cited by in corpus (5)
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- Iterative Bregman Projections for Regularized Transportation Problems
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- An efficient implementable inexact entropic proximal point algorithm for a class of linear programming problems
- Dual potentials for capacity constrained optimal transport