{
  "id": "2207.09788",
  "version": "v1",
  "published": "2022-07-20T10:05:07.000Z",
  "updated": "2022-07-20T10:05:07.000Z",
  "title": "Incremental Quasi-Newton Algorithms for Solving Nonconvex, Nonsmooth, Finite-Sum Optimization Problems",
  "authors": [
    "Gulcin Dinc Yalcin",
    "Frank E. Curtis"
  ],
  "categories": [
    "math.OC"
  ],
  "abstract": "Algorithms for solving nonconvex, nonsmooth, finite-sum optimization problems are proposed and tested. In particular, the algorithms are proposed and tested in the context of an optimization problem formulation arising in semi-supervised machine learning. The common feature of all algorithms is that they employ an incremental quasi-Newton (IQN) strategy, specifically an incremental BFGS (IBFGS) strategy. One applies an IBFGS strategy to the problem directly, whereas the others apply an IBFGS strategy to a difference-of-convex reformulation, smoothed approximation, or (strongly) convex local approximation. Experiments show that all IBFGS approaches fare well in practice, and all outperform a state-of-the-art bundle method.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2022-07-20T10:05:07.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "49M37",
      "65K05",
      "90C26",
      "90C30",
      "90C53"
    ],
    "keywords": [
      "finite-sum optimization problems",
      "incremental quasi-newton algorithms",
      "solving nonconvex",
      "ibfgs strategy",
      "optimization problem formulation"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}