{
  "id": "1602.08729",
  "version": "v1",
  "published": "2016-02-28T15:19:06.000Z",
  "updated": "2016-02-28T15:19:06.000Z",
  "title": "Asymmetric Forward-Backward-Adjoint Splitting for Solving Monotone Inclusions Involving Three Operators",
  "authors": [
    "Puya Latafat",
    "Panagiotis Patrinos"
  ],
  "categories": [
    "math.OC"
  ],
  "abstract": "In this work we propose a new splitting technique, namely Asymmetric Forward-Backward-Adjoint Splitting (AFBA), for solving monotone inclusions involving three terms, a maximally monotone, a cocoercive and a bounded linear operator. Classical operator splitting methods, like Douglas-Rachford (DRS) and Forward-Backward splitting (FBS) are special cases of our new algorithm. Among other things, AFBA unifies, extends and sheds light on the connections between many seemingly unrelated primal-dual algorithms for solving structured convex optimization problems, proposed in the recent years. More importantly AFBA greatly extends the scope and the applicability of splitting techniques to a wider variety of problems. One important special case leads to a generalization of the classical ADMM for problems with three (instead of two) blocks of variables.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2016-02-28T15:19:06.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "47H05",
      "65K05",
      "65K15",
      "90C25"
    ],
    "keywords": [
      "solving monotone inclusions",
      "asymmetric forward-backward-adjoint splitting",
      "solving structured convex optimization problems",
      "splitting technique",
      "important special case"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2016arXiv160208729L"
    }
  }
}