{
  "id": "2211.14852",
  "version": "v1",
  "published": "2022-11-27T15:08:22.000Z",
  "updated": "2022-11-27T15:08:22.000Z",
  "title": "Sufficient conditions for instability of the subgradient method with constant step size",
  "authors": [
    "Cédric Josz",
    "Lexiao Lai"
  ],
  "comment": "14 pages, 3 figures",
  "categories": [
    "math.OC"
  ],
  "abstract": "We provide sufficient conditions for instability of the subgradient method with constant step size around a local minimum of a locally Lipschitz semi-algebraic function. They are satisfied by several spurious local minima arising in robust principal component analysis and neural networks.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2022-11-27T15:08:22.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "constant step size",
      "subgradient method",
      "sufficient conditions",
      "instability",
      "local minimum"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 14,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}