{
  "id": "1710.05782",
  "version": "v1",
  "published": "2017-10-16T15:26:39.000Z",
  "updated": "2017-10-16T15:26:39.000Z",
  "title": "Second-Order Methods with Cubic Regularization Under Inexact Information",
  "authors": [
    "Saeed Ghadimi",
    "Han Liu",
    "Tong Zhang"
  ],
  "categories": [
    "math.OC"
  ],
  "abstract": "In this paper, we generalize (accelerated) Newton's method with cubic regularization under inexact second-order information for (strongly) convex optimization problems. Under mild assumptions, we provide global rate of convergence of these methods and show the explicit dependence of the rate of convergence on the problem parameters. While the complexity bounds of our presented algorithms are theoretically worse than those of their exact counterparts, they are at least as good as those of the optimal first-order methods. Our numerical experiments also show that using inexact Hessians can significantly speed up the algorithms in practice.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2017-10-16T15:26:39.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "cubic regularization",
      "second-order methods",
      "inexact information",
      "inexact second-order information",
      "optimal first-order methods"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}