{
  "id": "2205.04880",
  "version": "v1",
  "published": "2022-05-10T13:29:28.000Z",
  "updated": "2022-05-10T13:29:28.000Z",
  "title": "Consensus based optimization via jump-diffusion stochastic differential equations",
  "authors": [
    "D. Kalise",
    "A. Sharma",
    "M. V. Tretyakov"
  ],
  "categories": [
    "math.PR",
    "cs.NA",
    "math.NA",
    "math.OC"
  ],
  "abstract": "We introduce a new consensus based optimization (CBO) method where interacting particle system is driven by jump-diffusion stochastic differential equations. We study well-posedness of the particle system as well as of its mean-field limit. The major contributions of this paper are proofs of convergence of the interacting particle system towards the mean-field limit and convergence of a discretized particle system towards the continuous-time dynamics in the mean-square sense. We also prove convergence of the mean-field jump-diffusion SDEs towards global minimizer for a large class of objective functions. We demonstrate improved performance of the proposed CBO method over earlier CBO methods in numerical simulations on benchmark objective functions.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2022-05-10T13:29:28.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "60H10",
      "90C26",
      "65C30",
      "65C35",
      "60J76"
    ],
    "keywords": [
      "jump-diffusion stochastic differential equations",
      "interacting particle system",
      "optimization",
      "mean-field limit",
      "earlier cbo methods"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}