# Anderson Acceleration in Nonsmooth Problems: Local Convergence via Active Manifold Identification

arXiv: https://arxiv.org/abs/2410.09420 · HTML: https://mlsanity.com/paper/2410.09420/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Builds on 11 of its 39 references that are in the map.
- First posted on arXiv 12 Oct 2024.

## Builds on (most cited first, 11 of 11)

- [Coordinate Descent Algorithms](https://mlsanity.com/paper/1502.04759/) (2015)
- [A General Iterative Shrinkage and Thresholding Algorithm for Non-convex Regularized Optimization Problems](https://mlsanity.com/paper/1303.4434/) (2013)
- [Accelerated, Parallel and Proximal Coordinate Descent](https://mlsanity.com/paper/1312.5799/) (2013)
- [Douglas-Rachford splitting and ADMM for nonconvex optimization: tight convergence results](https://mlsanity.com/paper/1709.05747/) (2017)
- [Regularized Nonlinear Acceleration](https://mlsanity.com/paper/1606.04133/) (2016)
- [Anderson Acceleration of Proximal Gradient Methods](https://mlsanity.com/paper/1910.08590/) (2019)
- [Anderson Accelerated Douglas-Rachford Splitting](https://mlsanity.com/paper/1908.11482/) (2019)
- [Model Consistency of Partly Smooth Regularizers](https://mlsanity.com/paper/1405.1004/) (2014)
- [Anderson Acceleration for Nonconvex ADMM Based on Douglas-Rachford Splitting](https://mlsanity.com/paper/2006.14539/) (2020)
- [Anderson acceleration of coordinate descent](https://mlsanity.com/paper/2011.10065/) (2020)
- [Anderson Acceleration for Nonsmooth Fixed Point Problems](https://mlsanity.com/paper/2209.10336/) (2022)

## Abstract (arXiv)

Anderson acceleration is an effective technique for enhancing the efficiency of fixed-point iterations; however, analyzing its convergence in nonsmooth settings presents significant challenges. In this paper, we investigate a class of nonsmooth optimization algorithms characterized by the active manifold identification property. This class includes a diverse array of methods such as the proximal point method, proximal gradient method, proximal linear method, proximal coordinate descent method, Douglas-Rachford splitting (or the alternating direction method of multipliers), and the iteratively reweighted ℓ1 method, among others. Under the assumption that the optimization problem possesses an active manifold at a stationary point, we establish a local R-linear convergence rate for the Anderson-accelerated algorithm. Our extensive numerical experiments further highlight the robust performance of the proposed Anderson-accelerated methods.