{
  "id": "2109.06771",
  "version": "v1",
  "published": "2021-09-14T15:37:29.000Z",
  "updated": "2021-09-14T15:37:29.000Z",
  "title": "Resolvent of the parallel composition and proximity operator of the infimal postcomposition",
  "authors": [
    "Luis Briceño-Arias",
    "Fernando Roldán"
  ],
  "categories": [
    "math.OC"
  ],
  "abstract": "In this paper we provide the resolvent computation of the infimal postcomposition of a maximally monotone operator by a linear operator under mild assumptions. Connections with a modification of the warped resolvent are provided. In the context of convex optimization, we obtain the proximity operator of the infimal postcomposition of a convex function by a linear operator and we extend full range conditions on the linear operator to mild qualification conditions. We also introduce a generalization of the proximity operator involving a general linear bounded operator leading to a generalization of Moreau's decomposition for composite convex optimization.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2021-09-14T15:37:29.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "47H05",
      "47H10",
      "65K05",
      "65K15",
      "90C25",
      "49M29"
    ],
    "keywords": [
      "proximity operator",
      "infimal postcomposition",
      "parallel composition",
      "linear operator",
      "linear bounded operator leading"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}