{
  "id": "math/0607604",
  "version": "v1",
  "published": "2006-07-24T18:53:41.000Z",
  "updated": "2006-07-24T18:53:41.000Z",
  "title": "Characterization of the optimal plans for the Monge-Kantorovich transport problem",
  "authors": [
    "Christian Léonard"
  ],
  "comment": "39 pages",
  "categories": [
    "math.OC",
    "math.PR"
  ],
  "abstract": "We present a general method, based on conjugate duality, for solving a convex minimization problem without assuming unnecessary topological restrictions on the constraint set. It leads to dual equalities and characterizations of the minimizers without constraint qualification. As an example of application, the Monge-Kantorovich optimal transport problem is solved in great detail. In particular, the optimal transport plans are characterized without restriction. This characterization improves the already existing literature on the subject.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2006-07-24T18:53:41.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "46N10",
      "49J45",
      "28A35"
    ],
    "keywords": [
      "monge-kantorovich transport problem",
      "optimal plans",
      "characterization",
      "monge-kantorovich optimal transport problem",
      "optimal transport plans"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 39,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2006math......7604L"
    }
  }
}