{"ID":2899709,"CreatedAt":"2026-06-01T04:54:23.091178241Z","UpdatedAt":"2026-06-01T04:54:23.091178241Z","DeletedAt":null,"paper_url":"https://arxiv.org/abs/2507.00871","arxiv_id":"2507.00871","title":"Swarm-based optimization with jumps: a kinetic BGK framework and convergence analysis","abstract":"Metaheuristic algorithms are powerful tools for global optimization, particularly for non-convex and non-differentiable problems where exact methods are often impractical. Particle-based optimization methods, inspired by swarm intelligence principles, have shown effectiveness due to their ability to balance exploration and exploitation within the search space. In this work, we introduce a novel particle-based optimization algorithm where velocities are updated via random jumps, a strategy commonly used to enhance stochastic exploration. We formalize this approach by describing the dynamics through a kinetic modelling of BGK type, offering a unified framework that accommodates general noise distributions, including heavy-tailed ones like Cauchy. Under suitable parameter scaling, the model reduces to the Consensus-Based Optimization (CBO) dynamics. For non-degenerate Gaussian noise in bounded domains, we prove propagation of chaos and convergence towards minimizers. Numerical results on benchmark problems validate the approach and highlight its connection to CBO.","short_abstract":"Metaheuristic algorithms are powerful tools for global optimization, particularly for non-convex and non-differentiable problems where exact methods are often impractical. Particle-based optimization methods, inspired by swarm intelligence principles, have shown effectiveness due to their ability to balance exploration...","url_abs":"https://arxiv.org/abs/2507.00871","url_pdf":"https://arxiv.org/pdf/2507.00871v2","authors":"[\"Giacomo Borghi\",\"Hyesung Im\",\"Lorenzo Pareschi\"]","published":"2025-07-01T15:34:53Z","proceeding":"math.OC","tasks":"[\"math.OC\",\"math.NA\"]","methods":"[\"LoRA\"]","has_code":false}