{"ID":22918756,"CreatedAt":"2026-09-17T01:02:08.507062015Z","UpdatedAt":"2026-09-20T18:11:56.143995915Z","DeletedAt":null,"paper_url":"https://arxiv.org/abs/2609.17784","arxiv_id":"2609.17784","title":"Centroids for weak optimal transport with barycentric cost","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.","short_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...","url_abs":"https://arxiv.org/abs/2609.17784","url_pdf":"https://arxiv.org/pdf/2609.17784v1","authors":"[\"Friedemann Krannich\"]","published":"2026-09-15T19:50:07Z","proceeding":"math.OC","tasks":"[\"math.OC\",\"math.PR\"]","methods":"[]","has_code":false}