{
  "id": "2403.07295",
  "version": "v1",
  "published": "2024-03-12T03:56:13.000Z",
  "updated": "2024-03-12T03:56:13.000Z",
  "title": "Tight error bounds for log-determinant cones without constraint qualifications",
  "authors": [
    "Ying Lin",
    "Scott B. Lindstrom",
    "Bruno F. Lourenço",
    "Ting Kei Pong"
  ],
  "comment": "32 pages, comments welcome",
  "categories": [
    "math.OC",
    "cs.NA",
    "math.NA"
  ],
  "abstract": "In this paper, without requiring any constraint qualifications, we establish tight error bounds for the log-determinant cone, which is the closure of the hypograph of the perspective function of the log-determinant function. This error bound is obtained using the recently developed framework based on one-step facial residual functions.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2024-03-12T03:56:13.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "90C25",
      "52A20"
    ],
    "keywords": [
      "constraint qualifications",
      "log-determinant cone",
      "one-step facial residual functions",
      "establish tight error bounds",
      "log-determinant function"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 32,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}