Capacity-Constrained Wasserstein Barycenters: Existence, Duality, and Entropic Regularization
Abstract
We introduce a capacity-constrained Wasserstein barycenter problem in which each transport plan from an input measure to the barycenter is bounded by a prescribed capacity measure. On compact domains, we prove existence of capacity-constrained barycenters and establish a strong duality formula. We then study an entropy-regularized version under bounded capacity-density assumptions. The regularized problem has a unique optimal tuple of transport plans and a unique barycenter, while its dual involves an explicit capped-exponential penalty. Whenever dual maximizers exist, the optimal densities satisfy a capacity-clipped Gibbs formula. Finally, we prove an O(ε) estimate for the optimal values and show that the regularized plans converge to the minimum-entropy optimal solution of the unregularized problem.
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BibTeX
@misc{gamage2026capacityconstrained,
title = {{Capacity-Constrained Wasserstein Barycenters: Existence, Duality, and Entropic Regularization}},
author = {Chamila Gamage},
howpublished = {arXiv},
year = {2026},
month = sep,
doi = {10.48550/arxiv.2609.19054},
eprint = {2609.19054},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2609.19054},
note = {CC BY 4.0},
}
RIS
TY - UNPB
TI - Capacity-Constrained Wasserstein Barycenters: Existence, Duality, and Entropic Regularization
AU - Chamila Gamage
PY - 2026
DA - 2026/09/01
PB - arXiv
DO - 10.48550/arxiv.2609.19054
UR - https://arxiv.org/abs/2609.19054
AB - We introduce a capacity-constrained Wasserstein barycenter problem in which each transport plan from an input measure to the barycenter is bounded by a prescribed capacity measure. On compact domains, we prove existence of capacity-constrained barycenters and establish a strong duality formula. We then study an entropy-regularized version under bounded capacity-density assumptions. The regularized problem has a unique optimal tuple of transport plans and a unique barycenter, while its dual involves an explicit capped-exponential penalty. Whenever dual maximizers exist, the optimal densities satisfy a capacity-clipped Gibbs formula. Finally, we prove an O(ε) estimate for the optimal values and show that the regularized plans converge to the minimum-entropy optimal solution of the unregularized problem.
ER -