{
  "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.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2609.19054",
  "author_total": 1,
  "authors": [
    {
      "name": "Chamila Gamage"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/80n4jestdpdy9.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2609.19054",
  "fulltext_url": null,
  "id": "80n4jestdpdy9",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2609.19054",
  "language": null,
  "licence": "CC-BY-4.0",
  "licence_label": "CC BY 4.0",
  "licence_source": "article",
  "licence_url": "http://creativecommons.org/licenses/by/4.0/",
  "metadata_licence": "CC0-1.0",
  "native_subjects": [
    [
      "arxiv",
      "math.OC"
    ],
    [
      "openalex",
      "2604|Geometric Analysis and Curvature Flows"
    ]
  ],
  "openalex": "W7213529831",
  "pdf_url": "https://arxiv.org/pdf/2609.19054",
  "pmcid": null,
  "pmid": null,
  "published": "2026-09-01",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/80n4jestdpdy9.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:22:04Z",
      "native_id": "2609.19054",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2609.19054"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "arxiv:math.OC",
      "subfield": "optimisation-control"
    }
  ],
  "title": "Capacity-Constrained Wasserstein Barycenters: Existence, Duality, and Entropic Regularization",
  "title_text": "Capacity-Constrained Wasserstein Barycenters: Existence, Duality, and Entropic Regularization",
  "type": "preprint",
  "updated_at": "2026-10-30T12:22:04Z",
  "url": "https://research.draconitic.com/paper/80n4jestdpdy9",
  "venue": "arXiv",
  "versions": []
}