{
  "id": "2108.13994",
  "version": "v1",
  "published": "2021-08-31T17:40:03.000Z",
  "updated": "2021-08-31T17:40:03.000Z",
  "title": "Abstract strongly convergent variants of the proximal point algorithm",
  "authors": [
    "Andrei Sipos"
  ],
  "categories": [
    "math.OC",
    "math.LO"
  ],
  "abstract": "We prove an abstract form of the strong convergence of the Halpern-type and Tikhonov-type proximal point algorithms in CAT(0) spaces. In addition, we derive uniform and computable rates of metastability (in the sense of Tao) for these iterations using proof mining techniques.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2021-08-31T17:40:03.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "90C25",
      "46N10",
      "47J25",
      "47H09",
      "03F10"
    ],
    "keywords": [
      "abstract strongly convergent variants",
      "tikhonov-type proximal point algorithms",
      "abstract form",
      "strong convergence",
      "proof mining techniques"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}