{
  "id": "1609.02762",
  "version": "v1",
  "published": "2016-09-09T12:30:23.000Z",
  "updated": "2016-09-09T12:30:23.000Z",
  "title": "Convergence rates of moment-sum-of-squares hierarchies for optimal control problems",
  "authors": [
    "Milan Korda",
    "Didier Henrion",
    "Colin N. Jones"
  ],
  "categories": [
    "math.OC"
  ],
  "abstract": "We study the convergence rate of moment-sum-of-squares hierarchies of semidefinite programs for optimal control problems with polynomial data. It is known that these hierarchies generate polynomial under-approximations to the value function of the optimal control problem and that these under-approximations converge in the L1 norm to the value function as their degree d tends to infinity. We show that the rate of this convergence is O(1/ log log d). We treat in detail the continuous-time infinite-horizon discounted problem and describe in brief how the same rate can be obtained for the finite-horizon continuous-time problem and for the discrete-time counterparts of both problems.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2016-09-09T12:30:23.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "optimal control problem",
      "moment-sum-of-squares hierarchies",
      "convergence rate",
      "hierarchies generate polynomial under-approximations",
      "value function"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}