{
  "id": "1612.06965",
  "version": "v1",
  "published": "2016-12-21T03:37:03.000Z",
  "updated": "2016-12-21T03:37:03.000Z",
  "title": "Quasi-Newton Methods: Superlinear Convergence Without Line Search for Self-Concordant Functions",
  "authors": [
    "Wenbo Gao",
    "Donald Goldfarb"
  ],
  "comment": "16 pages, 2 figures",
  "categories": [
    "math.OC"
  ],
  "abstract": "We derive a \\emph{curvature-adaptive} step size for gradient-based iterative methods, including quasi-Newton methods, for minimizing self-concordant functions. This step size has a simple expression that can be computed analytically; hence, line searches are not needed. We show that using this step size in the BFGS method (and quasi-Newton methods generally) results in superlinear convergence for strongly convex self-concordant functions. We present numerical experiments comparing gradient descent and BFGS methods using the curvature-adaptive step size to traditional methods on logistic regression problems.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2016-12-21T03:37:03.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "90C53",
      "90C30"
    ],
    "keywords": [
      "quasi-newton methods",
      "superlinear convergence",
      "line search",
      "step size",
      "bfgs method"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 16,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}