{
  "id": "1608.02240",
  "version": "v1",
  "published": "2016-08-07T16:44:52.000Z",
  "updated": "2016-08-07T16:44:52.000Z",
  "title": "The forward-backward algorithm and the normal problem",
  "authors": [
    "Walaa M. Moursi"
  ],
  "categories": [
    "math.OC",
    "math.NA"
  ],
  "abstract": "The forward-backward splitting technique is a popular method for solving monotone inclusions that has applications in optimization. In this paper we explore the behaviour of the algorithm when the inclusion problem has no solution. We present a new formula to define the normal solutions using the forward-backward operator. We also provide a formula for the range of the displacement map of the forward-backward operator. Several examples illustrate our theory.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2016-08-07T16:44:52.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "47H09",
      "49M27",
      "65K10",
      "47H05",
      "47H14",
      "49M29",
      "49N19"
    ],
    "keywords": [
      "normal problem",
      "forward-backward algorithm",
      "forward-backward operator",
      "examples illustrate",
      "popular method"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}