{
  "id": "1909.05517",
  "version": "v1",
  "published": "2019-09-12T09:05:57.000Z",
  "updated": "2019-09-12T09:05:57.000Z",
  "title": "Barycenters in generalized Wasserstein spaces",
  "authors": [
    "Nhan-Phu Chung",
    "Thanh-Son Trinh"
  ],
  "comment": "18 pages. Comments welcome",
  "categories": [
    "math.OC",
    "math.FA"
  ],
  "abstract": "In 2014, Piccoli and Rossi introduced generalized Wasserstein spaces which are combinations of Wasserstein distances and $L^1$-distances [11]. In this article, we follow the ideas of Agueh and Carlier [1] to study generalized Wasserstein barycenters. We show the existence of barycenters for measures with compact supports. We also investigate a dual problem of the barycenter problem via our Kantorovich duality formula for generalized Wasserstein distances. Finally, we provide consistency of the barycenters.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2019-09-12T09:05:57.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "generalized wasserstein spaces",
      "kantorovich duality formula",
      "study generalized wasserstein barycenters",
      "barycenter problem",
      "dual problem"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 18,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}