{
  "id": "2401.00542",
  "version": "v1",
  "published": "2023-12-31T17:08:20.000Z",
  "updated": "2023-12-31T17:08:20.000Z",
  "title": "A relaxation viewpoint to Unbalanced Optimal Transport: duality, optimality and Monge formulation",
  "authors": [
    "Giuseppe Savaré",
    "Giacomo Enrico Sodini"
  ],
  "comment": "57 pages",
  "categories": [
    "math.OC",
    "math.FA"
  ],
  "abstract": "We present a general convex relaxation approach to study a wide class of Unbalanced Optimal Transport problems for finite non-negative measures with possibly different masses. These are obtained as the lower semicontinuous and convex envelope of a cost for non-negative Dirac masses. New general primal-dual formulations, optimality conditions, and metric-topological properties are carefully studied and discussed.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2023-12-31T17:08:20.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "49Q22",
      "28A33",
      "49K27"
    ],
    "keywords": [
      "monge formulation",
      "relaxation viewpoint",
      "optimality",
      "general convex relaxation approach",
      "unbalanced optimal transport problems"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 57,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}