{
  "id": "1604.05648",
  "version": "v1",
  "published": "2016-04-19T16:57:27.000Z",
  "updated": "2016-04-19T16:57:27.000Z",
  "title": "A consensus-based model for global optimization and its mean-field limit",
  "authors": [
    "Stephan Martin",
    "René Pinnau",
    "Claudia Totzeck",
    "Oliver Tse"
  ],
  "categories": [
    "math.PR",
    "math.OC"
  ],
  "abstract": "We introduce a new first-order stochastic swarm intelligence (SI) model in the spirit of consensus formation models, which can be used for the global optimization of a function in multiple dimensions. The SI model allows to perform the mean-field limit, which results in a nonstandard, nonlocal parabolic partial differential equation (PDE). Exploiting tools from PDE analysis we can show some convergence results that help to understand the asymptotic behavior of the SI model. We further present numerical investigations underlining the feasibility of our approach.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2016-04-19T16:57:27.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "mean-field limit",
      "global optimization",
      "consensus-based model",
      "nonlocal parabolic partial differential equation",
      "first-order stochastic swarm intelligence"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2016arXiv160405648M"
    }
  }
}