{
  "id": "2406.09786",
  "version": "v1",
  "published": "2024-06-14T07:35:16.000Z",
  "updated": "2024-06-14T07:35:16.000Z",
  "title": "Convergence analysis of a regularized Newton method with generalized regularization terms for convex optimization problems",
  "authors": [
    "Yuya Yamakawa",
    "Nobuo Yamashita"
  ],
  "categories": [
    "math.OC"
  ],
  "abstract": "In this paper, we present a regularized Newton method (RNM) with generalized regularization terms for an unconstrained convex optimization problem. The generalized regularization includes the quadratic, cubic, and elastic net regularization as a special case. Therefore, the proposed method is a general framework that includes not only the classical and cubic RNMs but also a novel RNM with the elastic net. We show that the proposed RNM has the global $\\mathcal{O}(k^{-2})$ and local superlinear convergence, which are the same as those of the cubic RNM.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2024-06-14T07:35:16.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "convex optimization problem",
      "generalized regularization terms",
      "regularized newton method",
      "convergence analysis",
      "cubic rnm"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}