# Convergence analysis of the Halpern iteration with adaptive anchoring parameters

arXiv: https://arxiv.org/abs/2505.10807 · HTML: https://mlsanity.com/paper/2505.10807/

## Key facts

- Cited by 2 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 16 May 2025.

## Built on by (most cited first, 2 of 2)

- [Solving Stochastic Fixed-Point Equations with High Probability](https://mlsanity.com/paper/2607.09097/) (2026)
- [Provable Parameter-Free Fixed-Point Algorithms with Linear Convergence Rates](https://mlsanity.com/paper/2608.09022/) (2026)

## Abstract (arXiv)

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.