{
  "abstract": "Particle swarm optimization (PSO) is a popular class of gradient-free methods for global optimization. We study a continuous-time model for momentum-free PSO with personal-best memory and global-best interaction. Unlike previous models which rely on smooth approximations, we keep the original discontinuous personal- and global-best processes. We study the small-step limit and show that weak limit points satisfy a stochastic differential inclusion: personal-best variables obey a relaxed record condition, while fast switching of the global-best selector leads to a convexified interaction. We then give conditions under which the true original selectors are recovered. Under suitable regularity and nondegeneracy assumptions, Brownian noise allows us to identify the personal-best processes with the latest record positions of the limiting trajectories and to prove that the particle attaining the global best is unique at almost every time. The resulting continuous-time dynamics retain both selection rules without smoothing them.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2610.07373",
  "author_total": 3,
  "authors": [
    {
      "name": "Pascal Bianchi"
    },
    {
      "name": "Radu-Alexandru Dragomir"
    },
    {
      "name": "Yerkin Yesbay"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/2rgd5hy7zq624.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2610.07373",
  "fulltext_url": null,
  "id": "2rgd5hy7zq624",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2610.07373",
  "language": null,
  "licence": "LicenseRef-arXiv-nonexclusive-1.0",
  "licence_label": "arXiv licence",
  "licence_source": "article",
  "licence_url": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
  "metadata_licence": "CC0-1.0",
  "native_subjects": [
    [
      "arxiv",
      "math.OC"
    ],
    [
      "openalex",
      "1702|Metaheuristic Optimization Algorithms Research"
    ]
  ],
  "openalex": "W7221041995",
  "pdf_url": "https://arxiv.org/pdf/2610.07373",
  "pmcid": null,
  "pmid": null,
  "published": "2026-10-21",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/2rgd5hy7zq624.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:34:22Z",
      "native_id": "2610.07373",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2610.07373"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "arxiv:math.OC",
      "subfield": "optimisation-control"
    }
  ],
  "title": "A continuous-time limit for particle swarm optimization",
  "title_text": "A continuous-time limit for particle swarm optimization",
  "type": "preprint",
  "updated_at": "2026-10-30T12:34:22Z",
  "url": "https://research.draconitic.com/paper/2rgd5hy7zq624",
  "venue": "arXiv",
  "versions": []
}