{
  "id": "1712.04825",
  "version": "v1",
  "published": "2017-12-13T15:47:55.000Z",
  "updated": "2017-12-13T15:47:55.000Z",
  "title": "Explicit bounds for Lipschitz constant of solution to basic problem in calculus of variations",
  "authors": [
    "Miguel Oliveira",
    "Georgi Smirnov"
  ],
  "comment": "16 pages",
  "categories": [
    "math.OC"
  ],
  "abstract": "In this paper we present explicit estimate for Lipschitz constant of solution to a problem of calculus of variations. The approach we use is due to Gamkrelidze and is based on the equivalence of the problem of calculus of variations and a time-optimal control problem. The obtained estimate is used to compute complexity bounds for a path-following method applied to a convex problem of calculus of variations with polyhedral end-point constraints.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2017-12-13T15:47:55.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "49J24",
      "49M15",
      "49M37",
      "49N60"
    ],
    "keywords": [
      "lipschitz constant",
      "explicit bounds",
      "basic problem",
      "variations",
      "time-optimal control problem"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 16,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}