{
  "id": "1307.2786",
  "version": "v1",
  "published": "2013-07-10T13:28:57.000Z",
  "updated": "2013-07-10T13:28:57.000Z",
  "title": "On the Efficient Gerschgorin Inclusion Usage in the Global Optimization αBB Method",
  "authors": [
    "Milan Hladík"
  ],
  "categories": [
    "math.OC"
  ],
  "abstract": "In this paper, we revisit the {\\alpha}BB method for solving global optimization problems. We investigate optimality of the scaling vector used in Gerschgorin's inclusion theorem to calculate bounds on the eigenvalues of the Hessian matrix. We propose two heuristics to compute good scaling vector d, and state three necessary optimality conditions for optimal d. Since the scaling vector calculated by the second presented method satisfies all three optimality conditions, it serves as a cheap but efficient solution.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2013-07-10T13:28:57.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "90C26",
      "G.1.6"
    ],
    "keywords": [
      "efficient gerschgorin inclusion usage",
      "scaling vector",
      "gerschgorins inclusion theorem",
      "solving global optimization problems",
      "necessary optimality conditions"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2013arXiv1307.2786H"
    }
  }
}