{
  "id": "2211.14850",
  "version": "v1",
  "published": "2022-11-27T15:06:29.000Z",
  "updated": "2022-11-27T15:06:29.000Z",
  "title": "Lyapunov stability of the subgradient method with constant step size",
  "authors": [
    "Cédric Josz",
    "Lexiao Lai"
  ],
  "comment": "11 pages, 2 figures",
  "categories": [
    "math.OC"
  ],
  "abstract": "We consider the subgradient method with constant step size for minimizing locally Lipschitz semi-algebraic functions. In order to analyze the behavior of its iterates in the vicinity of a local minimum, we introduce a notion of discrete Lyapunov stability and propose necessary and sufficient conditions for stability.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2022-11-27T15:06:29.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "constant step size",
      "subgradient method",
      "minimizing locally lipschitz semi-algebraic functions",
      "discrete lyapunov stability",
      "sufficient conditions"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 11,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}