{
  "id": "1809.07180",
  "version": "v1",
  "published": "2018-09-17T18:11:28.000Z",
  "updated": "2018-09-17T18:11:28.000Z",
  "title": "Projective Splitting with Forward Steps only Requires Continuity",
  "authors": [
    "Patrick R. Johnstone",
    "Jonathan Eckstein"
  ],
  "comment": "15 pages. arXiv admin note: text overlap with arXiv:1803.07043",
  "categories": [
    "math.OC",
    "cs.LG",
    "cs.NA"
  ],
  "abstract": "A recent innovation in projective splitting algorithms for monotone operator inclusions has been the development of a procedure using two forward steps instead of the customary proximal steps for operators that are Lipschitz continuous. This paper shows that the Lipschitz assumption is unnecessary when the forward steps are performed in finite-dimensional spaces: a backtracking linesearch yields a convergent algorithm for operators that are merely continuous with full domain.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2018-09-17T18:11:28.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "forward steps",
      "continuity",
      "customary proximal steps",
      "monotone operator inclusions",
      "finite-dimensional spaces"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 15,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}