{
  "id": "2006.08743",
  "version": "v1",
  "published": "2020-06-15T20:25:03.000Z",
  "updated": "2020-06-15T20:25:03.000Z",
  "title": "Penalization of barycenters for $\\varphi$-exponential distributions",
  "authors": [
    "S. Kum",
    "M. H. Duong",
    "Y. Lim",
    "S. Yun"
  ],
  "comment": "24 pages",
  "categories": [
    "math.OC",
    "cs.NA",
    "math.NA"
  ],
  "abstract": "In this paper we study the penalization of barycenters in the Wasserstein space for $\\varphi$-exponential distributions. We obtain an explicit characterization of the barycenter in terms of the variances of the measures generalizing existing results for Gaussian measures. We then develop a gradient projection method for the computation of the barycenter establishing a Lipstchitz continuity for the gradient function. We also numerically show the influence of parameters and stability of the algorithm under small perturbation of data.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2020-06-15T20:25:03.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "exponential distributions",
      "barycenter",
      "penalization",
      "gradient projection method",
      "lipstchitz continuity"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 24,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}