{
  "id": "2311.13092",
  "version": "v1",
  "published": "2023-11-22T01:44:00.000Z",
  "updated": "2023-11-22T01:44:00.000Z",
  "title": "State-Dependent Sweeping Processes: Asymptotic Behavior and Algorithmic Approaches",
  "authors": [
    "Samir Adly",
    "Monica G. Cojocaru",
    "Ba Khiet Le"
  ],
  "categories": [
    "math.OC"
  ],
  "abstract": "In this paper, we investigate the asymptotic properties of a particular class of state-dependent sweeping processes. While extensive research has been conducted on the existence and uniqueness of solutions for sweeping processes, there is a scarcity of studies addressing their behavior in the limit of large time. Additionally, we introduce novel algorithms designed for the resolution of quasi-variational inequalities. As a result, we introduce a new derivative-free algorithm to find zeros of nonsmooth Lipschitz continuous mappings with a linear convergence rate. This algorithm can be effectively used in nonsmooth and nonconvex optimization problems that do not possess necessarily second-order differentiability conditions of the data.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2023-11-22T01:44:00.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "28B05",
      "34A36",
      "34A60",
      "49J52",
      "49J53",
      "93D20"
    ],
    "keywords": [
      "state-dependent sweeping processes",
      "algorithmic approaches",
      "asymptotic behavior",
      "possess necessarily second-order differentiability conditions",
      "nonconvex optimization problems"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}