A derivative-free particle method for optimization in Hilbert spaces
Fuente:
arXiv
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| Autores principales: | , |
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| Formato: | Preprint |
| Publicado: |
2026
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| Acceso en línea: | |
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| _version_ | 1866916066752462848 |
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| author | Huang, Hui Kouhkouh, Hicham |
| author_facet | Huang, Hui Kouhkouh, Hicham |
| contents | We introduce a stochastic interacting particle system in separable Hilbert spaces together with its associated mean-field formulation. The model is shown to retain the characteristic consensus-driven structure of classical Consensus-Based Optimization, while accounting for the analytical challenges of infinite-dimensional dynamics. We establish well-posedness of the proposed dynamics and analyze the associated consensus mechanism. Furthermore, we derive convergence guarantees under suitable assumptions on the objective functional, showing concentration of the dynamics toward the minimizer in the long-time regime. This extends the applicability of the method to a broad class of infinite-dimensional optimization problems. In addition, we study the corresponding finite-particle system relevant for numerical implementation and propose a practical algorithm. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2605_31565 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | A derivative-free particle method for optimization in Hilbert spaces Huang, Hui Kouhkouh, Hicham Optimization and Control Dynamical Systems We introduce a stochastic interacting particle system in separable Hilbert spaces together with its associated mean-field formulation. The model is shown to retain the characteristic consensus-driven structure of classical Consensus-Based Optimization, while accounting for the analytical challenges of infinite-dimensional dynamics. We establish well-posedness of the proposed dynamics and analyze the associated consensus mechanism. Furthermore, we derive convergence guarantees under suitable assumptions on the objective functional, showing concentration of the dynamics toward the minimizer in the long-time regime. This extends the applicability of the method to a broad class of infinite-dimensional optimization problems. In addition, we study the corresponding finite-particle system relevant for numerical implementation and propose a practical algorithm. |
| title | A derivative-free particle method for optimization in Hilbert spaces |
| topic | Optimization and Control Dynamical Systems |
| url | https://arxiv.org/abs/2605.31565 |