# Preconditioned Halpern iteration with adaptive anchoring parameters and an acceleration to Chambolle--Pock algorithm

arXiv: https://arxiv.org/abs/2506.22725 · HTML: https://mlsanity.com/paper/2506.22725/

## Key facts

- Cited by 1 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 28 Jun 2025.

## Built on by (most cited first, 1 of 1)

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

## Abstract (arXiv)

In this article, we propose a preconditioned Halpern iteration with adaptive anchoring parameters (PHA) by integrating a preconditioner and Halpern iteration with adaptive anchoring parameters. Then we establish the strong convergence and at least O(1/k) convergence rate of the PHA method, and extend these convergence results to Halpern-type preconditioned proximal point method with adaptive anchoring parameters. Moreover, we develop an accelerated Chambolle--Pock algorithm that is shown to have at least O(1/k) convergence rate concerning the residual mapping and the primal-dual gap. Finally, numerical experiments on the minimax matrix game and LASSO problem are provided to show the performance of our proposed algorithms.