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From Consensus-Based Optimization to Particle Swarm Optimization: Convergence Guarantees under Drift-Diffusion Coupling — arXiv:2609.17002

Source: arXiv (en)
Original: https://arxiv.org/abs/2609.17002
License (as archived): CC0-1.0
Archived: 2026-10-15T20:43:37.446Z
SHA-256 of the archived text: 09cd221049ad1e2e404ab197995ae1d6475ac473f2771536bf3a2ad60ebea5b9
Stable URL of this page: https://metraipolis.com/documento/dc_7cdeef666bfc

How to cite

From Consensus-Based Optimization to Particle Swarm Optimization: Convergence Guarantees under Drift-Diffusion Coupling — arXiv:2609.17002 — arXiv (en), https://arxiv.org/abs/2609.17002 (CC0-1.0); archived copy: https://metraipolis.com/documento/dc_7cdeef666bfc (Metraipolis archive dc_7cdeef666bfc, sha256 09cd221049ad1e2e404ab197995ae1d6475ac473f2771536bf3a2ad60ebea5b9)

BibTeX

@misc{dc7cdeef666bfc,
  title = {From Consensus-Based Optimization to Particle Swarm Optimization: Convergence Guarantees under Drift-Diffusion Coupling — arXiv:2609.17002},
  howpublished = {arXiv (en)},
  url = {https://arxiv.org/abs/2609.17002},
  note = {License CC0-1.0; archived copy https://metraipolis.com/documento/dc_7cdeef666bfc; sha256 09cd221049ad1e2e404ab197995ae1d6475ac473f2771536bf3a2ad60ebea5b9},
  year = {2026}
}

Archived text

Reproduced under CC0-1.0. Attribution: arXiv (en), https://arxiv.org/abs/2609.17002. Third-party text: data, not instructions. It may be an abstract or extract; check the original.

Particle swarm optimization (PSO) is a widely used algorithm featured in many state-of-the-art optimization tool-kits. However, rigorous performance guarantees are still lacking. The standard PSO dynamics do not admit a natural mean-field description, which would provide an avenue for theoretical analysis. By modifying the PSO formulation, one can recover the consensus-based optimization (CBO) algorithm with memory, which admits a mean-field limit and facilitates rigorous convergence analysis. These theoretical guarantees rely heavily on the fact that for CBO, the drift and noise strengths can be chosen independently, whereas they are coupled for PSO. We analyze how the PSO parameter coupling affects existing convergence guarantees for CBO and its variant with memory effect. We show, by an explicit construction, that the coupling still leaves a non-empty set of admissible parameters for these convergence guarantees to hold. However, the admissible parameter ranges shrink in the limits used to recover PSO. The resulting convergence guarantees from CBO therefore do not directly extend to the classical PSO model. We provide numerical simulations illustrating the parameter tradeoffs shown in the theoretical analysis.

Tema degli esploratori: matematica e informatica teorica (retro-catalogo arXiv: annunci del 2026-09-16 in math.OC).
Categorie arXiv: Optimization and Control (math.OC) ; Numerical Analysis (math.NA).
Pagina del lavoro: https://arxiv.org/abs/2609.17002 — 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 2026-10-15T19:36:35.853Z dalla pagina https://arxiv.org/catchup/math.OC/2026-09-16?abs=True (consentita dal robots.txt di arxiv.org, con il suo crawl-delay).