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| Autores principales: | , , , |
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| Formato: | Preprint |
| Publicado: |
2025
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| Materias: | |
| Acceso en línea: | https://arxiv.org/abs/2505.10807 |
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| _version_ | 1866910947522641920 |
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| author | He, Songnian Xu, Hong-Kun Dong, Qiao-Li Mei, Na |
| author_facet | He, Songnian Xu, Hong-Kun Dong, Qiao-Li Mei, Na |
| contents | We propose an adaptive way to choose the anchoring parameters for the Halpern iteration to find a fixed point of a nonexpansive mapping in a real Hilbert space. We prove strong convergence of this adaptive Halpern iteration and obtain the rate of asymptotic regularity at least O(1/k), where k is the number of iterations. Numerical experiments are also provided to show advantages and outperformance of our adaptive Halpern algorithm over the standard Halpern algorithm. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2505_10807 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Convergence analysis of the Halpern iteration with adaptive anchoring parameters He, Songnian Xu, Hong-Kun Dong, Qiao-Li Mei, Na Optimization and Control We propose an adaptive way to choose the anchoring parameters for the Halpern iteration to find a fixed point of a nonexpansive mapping in a real Hilbert space. We prove strong convergence of this adaptive Halpern iteration and obtain the rate of asymptotic regularity at least O(1/k), where k is the number of iterations. Numerical experiments are also provided to show advantages and outperformance of our adaptive Halpern algorithm over the standard Halpern algorithm. |
| title | Convergence analysis of the Halpern iteration with adaptive anchoring parameters |
| topic | Optimization and Control |
| url | https://arxiv.org/abs/2505.10807 |