{
  "id": "2404.10372",
  "version": "v1",
  "published": "2024-04-16T08:10:15.000Z",
  "updated": "2024-04-16T08:10:15.000Z",
  "title": "Consensus-based algorithms for stochastic optimization problems",
  "authors": [
    "Sabrina Bonandin",
    "Michael Herty"
  ],
  "categories": [
    "math.OC"
  ],
  "abstract": "We address an optimization problem where the cost function is the expectation of a random mapping. To tackle the problem two approaches based on the approximation of the objective function by consensus-based particle optimization methods on the search space are developed. The resulting methods are mathematically analyzed using a mean-field approximation and their connection is established. Several numerical experiments show the validity of the proposed algorithms and investigate their rates of convergence.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2024-04-16T08:10:15.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "82B40",
      "65K10",
      "60K35"
    ],
    "keywords": [
      "stochastic optimization problems",
      "consensus-based algorithms",
      "consensus-based particle optimization methods",
      "cost function",
      "mean-field approximation"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}