{
  "abstract": "We generalize the theory of Wasserstein barycenters between N given measures from the Wasserstein distance to the weak optimal transport problem with barycentric cost. We find a multi-marginal formulation and its dual problem. The multi-marginal problem is new in itself; contrary to the classical multi-marginal optimal transport problem, the first M marginals of its competitors are not fixed but instead only need dominate the first M given measures in convex order, while the last N-M marginals of its competitors are dominated in convex order by the last N-M given measures.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2609.17784",
  "author_total": 1,
  "authors": [
    {
      "name": "Friedemann Krannich"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/4pd355qm8yy0c.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2609.17784",
  "fulltext_url": null,
  "id": "4pd355qm8yy0c",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2609.17784",
  "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"
    ],
    [
      "arxiv",
      "math.PR"
    ],
    [
      "openalex",
      "2604|Geometric Analysis and Curvature Flows"
    ]
  ],
  "openalex": "W7213502095",
  "pdf_url": "https://arxiv.org/pdf/2609.17784",
  "pmcid": null,
  "pmid": null,
  "published": "2026-09-15",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/4pd355qm8yy0c.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:22:04Z",
      "native_id": "2609.17784",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2609.17784"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "arxiv:math.OC",
      "subfield": "optimisation-control"
    },
    {
      "field": "mathematics",
      "origin": "arxiv:math.PR",
      "subfield": "probability"
    }
  ],
  "title": "Centroids for weak optimal transport with barycentric cost",
  "title_text": "Centroids for weak optimal transport with barycentric cost",
  "type": "preprint",
  "updated_at": "2026-10-30T12:22:04Z",
  "url": "https://research.draconitic.com/paper/4pd355qm8yy0c",
  "venue": "arXiv",
  "versions": []
}