Faithful global convergence for the rescaled Consensus-Based Optimization
Fuente:
arXiv
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| Autores principales: | , , |
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| Formato: | Preprint |
| Publicado: |
2025
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| Acceso en línea: | |
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| _version_ | 1866909992324431872 |
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| author | Huang, Hui Kouhkouh, Hicham Sun, Lukang |
| author_facet | Huang, Hui Kouhkouh, Hicham Sun, Lukang |
| contents | We analyze the Consensus-Based Optimization (CBO) algorithm with a consensus point rescaled by a small fixed parameter $κ\in (0,1)$. Under minimal assumptions on the objective function and the initial data, we establish its unconditional convergence to the global minimizer. Our results hold in the asymptotic regime where both the time--horizon $t \to \infty$ and the inverse--temperature $α\to \infty$, providing a rigorous theoretical foundation for the algorithm's global convergence. Furthermore, our findings extend to the case of multiple and non--discrete set of minimizers. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2503_08578 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Faithful global convergence for the rescaled Consensus-Based Optimization Huang, Hui Kouhkouh, Hicham Sun, Lukang Optimization and Control Analysis of PDEs We analyze the Consensus-Based Optimization (CBO) algorithm with a consensus point rescaled by a small fixed parameter $κ\in (0,1)$. Under minimal assumptions on the objective function and the initial data, we establish its unconditional convergence to the global minimizer. Our results hold in the asymptotic regime where both the time--horizon $t \to \infty$ and the inverse--temperature $α\to \infty$, providing a rigorous theoretical foundation for the algorithm's global convergence. Furthermore, our findings extend to the case of multiple and non--discrete set of minimizers. |
| title | Faithful global convergence for the rescaled Consensus-Based Optimization |
| topic | Optimization and Control Analysis of PDEs |
| url | https://arxiv.org/abs/2503.08578 |