{
  "abstract": "We study Gaussian-restricted barycenters for quadratic two-sided Kullback--Leibler unbalanced optimal transport with independent marginal penalties and no coupling entropy. Exact profiling of the barycenter mass reduces the problem to a smooth Gaussian shape functional with endogenous Gibbs weights. We establish global attainment, derive the stationary moment equations, and construct a reverse-KL majorization--minimization (MM) iteration whose full sequence converges from every nondegenerate Gaussian initialization to a stationary fixed point. The diagonal second variation induces a parallel-sum tensor coupling the Bures--Wasserstein and Fisher--Rao metrics; its finite-mass extension admits a radial cone representation. Under common penalty scaling, global minimizers converge to a Gaussian Wasserstein barycenter with effective weights; for sufficiently large penalties, the minimizer is unique and admits a first-order analytic expansion. In the small-penalty regime, the distance of every global minimizer to the compact maximizer set of a weighted Chernoff affinity functional vanishes with respect to the mean--covariance parameter distance. Numerical experiments illustrate MM descent, local contraction, and the two penalty limits.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2609.02870",
  "author_total": 2,
  "authors": [
    {
      "name": "Jiaping Yang"
    },
    {
      "name": "Yunxin Zhang"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/02be3fk7gnzmk.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2609.02870",
  "fulltext_url": null,
  "id": "02be3fk7gnzmk",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2609.02870",
  "language": null,
  "licence": "LicenseRef-arXiv-nonexclusive-1.0",
  "licence_label": "arXiv licence",
  "licence_source": "article",
  "licence_url": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
  "metadata_licence": "CC0-1.0",
  "native_subjects": [
    [
      "arxiv",
      "math.OC"
    ],
    [
      "openalex",
      "2604|Geometric Analysis and Curvature Flows"
    ]
  ],
  "openalex": "W7207705843",
  "pdf_url": "https://arxiv.org/pdf/2609.02870",
  "pmcid": null,
  "pmid": null,
  "published": "2026-09-02",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/02be3fk7gnzmk.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:18:20Z",
      "native_id": "2609.02870",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2609.02870"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "arxiv:math.OC",
      "subfield": "optimisation-control"
    }
  ],
  "title": "Gaussian-Restricted Barycenters for KL-Unbalanced Optimal Transport: Variational Theory and Fixed-Point Convergence",
  "title_text": "Gaussian-Restricted Barycenters for KL-Unbalanced Optimal Transport: Variational Theory and Fixed-Point Convergence",
  "type": "preprint",
  "updated_at": "2026-10-30T12:18:20Z",
  "url": "https://research.draconitic.com/paper/02be3fk7gnzmk",
  "venue": "arXiv",
  "versions": []
}