Well-posedness and mean-field limit estimate of a consensus-based algorithm for min-max problems
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arXiv
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| Auteurs principaux: | , |
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| Format: | Preprint |
| Publié: |
2026
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| _version_ | 1866918336655261696 |
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| author | Huang, Hui Warnett, Jethro |
| author_facet | Huang, Hui Warnett, Jethro |
| contents | The recent work arXiv:2407.17373 proposes a derivative-free consensus-based particle method that computes global solutions to nonconvex-nonconcave min-max problems and establishes global exponential convergence in the sense of the mean-field law. This paper aims to address the theoretical gaps in arXiv:2407.17373, specifically by providing a quantitative estimate of the mean-field limit with respect to the number of particles, as well as establishing the well-posedness of both the finite particle model and the corresponding mean-field dynamics. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2602_12886 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | Well-posedness and mean-field limit estimate of a consensus-based algorithm for min-max problems Huang, Hui Warnett, Jethro Optimization and Control 65C35, 65K05, 90C56, 35Q90, 35Q83 The recent work arXiv:2407.17373 proposes a derivative-free consensus-based particle method that computes global solutions to nonconvex-nonconcave min-max problems and establishes global exponential convergence in the sense of the mean-field law. This paper aims to address the theoretical gaps in arXiv:2407.17373, specifically by providing a quantitative estimate of the mean-field limit with respect to the number of particles, as well as establishing the well-posedness of both the finite particle model and the corresponding mean-field dynamics. |
| title | Well-posedness and mean-field limit estimate of a consensus-based algorithm for min-max problems |
| topic | Optimization and Control 65C35, 65K05, 90C56, 35Q90, 35Q83 |
| url | https://arxiv.org/abs/2602.12886 |