An interacting particle consensus method for constrained global optimization
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arXiv
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| Hauptverfasser: | , , , |
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| Format: | Preprint |
| Veröffentlicht: |
2024
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| _version_ | 1866917366634381312 |
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| author | Carrillo, José A. Jin, Shi Zhang, Haoyu Zhu, Yuhua |
| author_facet | Carrillo, José A. Jin, Shi Zhang, Haoyu Zhu, Yuhua |
| contents | This paper presents a particle-based optimization method designed for addressing minimization problems with equality constraints, particularly in cases where the loss function exhibits non-differentiability or non-convexity. The proposed method combines components from consensus-based optimization algorithm with a newly introduced forcing term directed at the constraint set. A rigorous mean-field limit of the particle system is derived, and the convergence of the mean-field limit to the constrained minimizer is established. Additionally, we introduce a stable discretized algorithm and conduct various numerical experiments to demonstrate the performance of the proposed method. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2405_00891 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | An interacting particle consensus method for constrained global optimization Carrillo, José A. Jin, Shi Zhang, Haoyu Zhu, Yuhua Optimization and Control Numerical Analysis Analysis of PDEs 90C56, 65C35, 35Q70, 82C22, 35Q84 This paper presents a particle-based optimization method designed for addressing minimization problems with equality constraints, particularly in cases where the loss function exhibits non-differentiability or non-convexity. The proposed method combines components from consensus-based optimization algorithm with a newly introduced forcing term directed at the constraint set. A rigorous mean-field limit of the particle system is derived, and the convergence of the mean-field limit to the constrained minimizer is established. Additionally, we introduce a stable discretized algorithm and conduct various numerical experiments to demonstrate the performance of the proposed method. |
| title | An interacting particle consensus method for constrained global optimization |
| topic | Optimization and Control Numerical Analysis Analysis of PDEs 90C56, 65C35, 35Q70, 82C22, 35Q84 |
| url | https://arxiv.org/abs/2405.00891 |