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arXiv · 2609.19054

Capacity-Constrained Wasserstein Barycenters: Existence, Duality, and Entropic Regularization

Chamila Gamage
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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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Chamila Gamage. 2026-07-21. Capacity-Constrained Wasserstein Barycenters: Existence, Duality, and Entropic Regularization. https://arxiv.org/abs/2609.19054

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