{
  "id": "0711.1268",
  "version": "v1",
  "published": "2007-11-08T13:05:26.000Z",
  "updated": "2007-11-08T13:05:26.000Z",
  "title": "Characterization of optimal Transport Plans for the Monge-Kantorovich-Problem",
  "authors": [
    "Walter Schachermayer",
    "Josef Teichmann"
  ],
  "comment": "to appear in Proceedings of the AMS",
  "categories": [
    "math.OC",
    "math.FA"
  ],
  "abstract": "We prove that $c$-cyclically monotone transport plans $\\pi$ optimize the Monge-Kantorovich transportation problem under an additional measurability condition. This measurability condition is always satisfied for finitely valued, lower semi-continuous cost functions. In particular, this yields a positive answer to Problem 2.25 in C. Villani's book. We emphasize that we do not need any regularity conditions as were imposed in the previous literature.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2007-11-08T13:05:26.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "49J45",
      "28A35"
    ],
    "keywords": [
      "optimal transport plans",
      "characterization",
      "monge-kantorovich-problem",
      "monge-kantorovich transportation problem",
      "lower semi-continuous cost functions"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2007arXiv0711.1268S"
    }
  }
}