{
  "id": "2008.04831",
  "version": "v1",
  "published": "2020-08-11T16:26:43.000Z",
  "updated": "2020-08-11T16:26:43.000Z",
  "title": "Random iterations of paracontraction maps and applications to feasibility problems",
  "authors": [
    "Edgar Matias",
    "Majela Pentón Machado"
  ],
  "categories": [
    "math.DS",
    "math.OC"
  ],
  "abstract": "In this paper, we consider the problem of finding an almost surely common fixed point of a family of paracontraction maps indexed on a probability space, which we refer to as the stochastic feasibility problem. We show that a random iteration of paracontraction maps driven by an ergodic stationary sequence converges, with probability one, to a solution of the stochastic feasibility problem, provided a solution exists. As applications, we obtain non-white noise randomized algorithms to solve the stochastic convex feasibility problem and the problem of finding an almost surely common zero of a collection of maximal monotone operators.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2020-08-11T16:26:43.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "random iteration",
      "stochastic feasibility problem",
      "applications",
      "ergodic stationary sequence converges",
      "stochastic convex feasibility problem"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}