# Anderson Acceleration for Nonsmooth Fixed Point Problems

arXiv: https://arxiv.org/abs/2209.10336 · HTML: https://mlsanity.com/paper/2209.10336/

## Key facts

- Cited by 3 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 21 Sep 2022.

## Built on by (most cited first, 3 of 3)

- [Improved Convergence Factor of Windowed Anderson Acceleration for Symmetric Fixed-Point Iterations](https://mlsanity.com/paper/2311.02490/) (2023)
- [Anderson acceleration for iteratively reweighted ℓ1 algorithm](https://mlsanity.com/paper/2403.07271/) (2024)
- [Anderson Acceleration in Nonsmooth Problems: Local Convergence via Active Manifold Identification](https://mlsanity.com/paper/2410.09420/) (2024)

## Abstract (arXiv)

We give new convergence results of Anderson acceleration for the composite max fixed point problem. We prove that Anderson(1) and EDIIS(1) are q-linear convergent with a smaller q-factor than existing q-factors. Moreover, we propose a smoothing approximation of the composite max function in the contractive fixed point problem. We show that the smoothing approximation is a contraction mapping with the same fixed point as the composite max fixed point problem. Our results rigorously confirm that the nonsmoothness does not affect the convergence rate of Anderson acceleration method when we use the proposed smoothing approximation for the composite max fixed point problem. Numerical results for constrained minimax problems, complementarity problems and nonsmooth differential equations are presented to show the efficiency and good performance of the proposed Anderson acceleration method with smoothing approximation.