Self-interacting CBO: Existence, uniqueness, and long-time convergence
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arXiv
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| Format: | Preprint |
| Published: |
2024
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| _version_ | 1866912120549933056 |
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| author | Huang, Hui Kouhkouh, Hicham |
| author_facet | Huang, Hui Kouhkouh, Hicham |
| contents | A self-interacting dynamics that mimics the standard Consensus-Based Optimization (CBO) model is introduced. This single-particle dynamics is shown to converge to a unique invariant measure that approximates the global minimum of a given function. As an application, its connection to CBO with Personal Best introduced by C. Totzeck and M.-T. Wolfram (Math. Biosci. Eng., 2020) has been established. |
| format | Preprint |
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arxiv_https___arxiv_org_abs_2411_10295 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Self-interacting CBO: Existence, uniqueness, and long-time convergence Huang, Hui Kouhkouh, Hicham Optimization and Control Probability 60H10, 65C35, 37N40, 90C26 A self-interacting dynamics that mimics the standard Consensus-Based Optimization (CBO) model is introduced. This single-particle dynamics is shown to converge to a unique invariant measure that approximates the global minimum of a given function. As an application, its connection to CBO with Personal Best introduced by C. Totzeck and M.-T. Wolfram (Math. Biosci. Eng., 2020) has been established. |
| title | Self-interacting CBO: Existence, uniqueness, and long-time convergence |
| topic | Optimization and Control Probability 60H10, 65C35, 37N40, 90C26 |
| url | https://arxiv.org/abs/2411.10295 |