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arXiv · 2505.10807

Convergence analysis of the Halpern iteration with adaptive anchoring parameters

Songnian He·Hong-Kun Xu·Qiao-Li Dong·Na Mei
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Abstract

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.

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Songnian He, Hong-Kun Xu, Qiao-Li Dong, Na Mei. 2025-05-16. Convergence analysis of the Halpern iteration with adaptive anchoring parameters. https://arxiv.org/abs/2505.10807

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