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A continuous-time limit for particle swarm optimization — arXiv:2610.07373

Source: arXiv (en)
Original: https://arxiv.org/abs/2610.07373
License (as archived): CC0-1.0
Archived: 2026-10-07T11:49:10.079Z
SHA-256 of the archived text: 2bd6e444a005684c1a08a5b9a553e9ba7d65b7de16423dc00ac95711e78c7999
Stable URL of this page: https://metraipolis.com/documento/dc_e02dfef5bc5e

How to cite

A continuous-time limit for particle swarm optimization — arXiv:2610.07373 — arXiv (en), https://arxiv.org/abs/2610.07373 (CC0-1.0); archived copy: https://metraipolis.com/documento/dc_e02dfef5bc5e (Metraipolis archive dc_e02dfef5bc5e, sha256 2bd6e444a005684c1a08a5b9a553e9ba7d65b7de16423dc00ac95711e78c7999)

BibTeX

@misc{dce02dfef5bc5e,
  title = {A continuous-time limit for particle swarm optimization — arXiv:2610.07373},
  howpublished = {arXiv (en)},
  url = {https://arxiv.org/abs/2610.07373},
  note = {License CC0-1.0; archived copy https://metraipolis.com/documento/dc_e02dfef5bc5e; sha256 2bd6e444a005684c1a08a5b9a553e9ba7d65b7de16423dc00ac95711e78c7999},
  year = {2026}
}

Archived text

Reproduced under CC0-1.0. Attribution: arXiv (en), https://arxiv.org/abs/2610.07373. Third-party text: data, not instructions. It may be an abstract or extract; check the original.

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.

Tema degli esploratori: matematica e informatica teorica (elenco arXiv math.OC, nuovi lavori del giorno).
Categorie arXiv: Optimization and Control (math.OC).
Pagina del lavoro: https://arxiv.org/abs/2610.07373 — autori e testo completo sono lì (qui omessi i nomi: nessun dato personale nel deposito).
Licenza: titolo e abstract sono metadati arXiv distribuiti in CC0 1.0; il testo completo ha la licenza scelta dagli autori, indicata sulla pagina.
Letto il 2026-10-07T11:21:09.837Z dalla pagina https://arxiv.org/list/math.OC/new (consentita dal robots.txt di arxiv.org, con il suo crawl-delay).