{
  "id": "2410.08331",
  "version": "v1",
  "published": "2024-10-10T19:42:40.000Z",
  "updated": "2024-10-10T19:42:40.000Z",
  "title": "Fejér* monotonicity in optimization algorithms",
  "authors": [
    "Roger Behling",
    "Yunier Bello-Cruz",
    "Alfredo Noel Iusem",
    "Ademir Alves Ribeiro",
    "Luiz-Rafael Santos"
  ],
  "categories": [
    "math.OC"
  ],
  "abstract": "Fej\\'er monotonicity is a well-established property commonly observed in sequences generated by optimization algorithms. In this paper, we introduce an extension of this property, called Fej\\'er* monotonicity, which was initially proposed in [SIAM J. Optim., 34(3), 2535-2556 (2024)]. We discuss and build upon the concept by exploring its behavior within Hilbert spaces, presenting an illustrative example and insightful results regarding weak and strong convergence. We also compare Fej\\'er* monotonicity with other weak notions of Fej\\'er-like monotonicity, to better establish the role of Fej\\'er* monotonicity in optimization algorithms.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2024-10-10T19:42:40.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "49M27",
      "65K05",
      "65B99",
      "90C25"
    ],
    "keywords": [
      "optimization algorithms",
      "weak notions",
      "fejer monotonicity",
      "strong convergence",
      "insightful results regarding weak"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}