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The derivative-free projection method (DFPM) is an efficient algorithm for solving monotone nonlinear equations. As problems grow larger, there is a strong demand for speeding up the convergence of DFPM. This paper considers the application…

Optimization and Control · Mathematics 2026-01-23 Jiachen Jin , Hongxia Wang , Kangkang Deng

In this work, we propose a generalized alternating Anderson acceleration method, a periodic scheme composed of $t$ fixed-point iteration steps, interleaved with $s$ steps of Anderson acceleration with window size $m$, to solve linear and…

Numerical Analysis · Mathematics 2026-02-02 Yunhui He , Santolo Leveque

The alternating direction multiplier method (ADMM) is widely used in computer graphics for solving optimization problems that can be nonsmooth and nonconvex. It converges quickly to an approximate solution, but can take a long time to…

Optimization and Control · Mathematics 2020-06-29 Wenqing Ouyang , Yue Peng , Yuxin Yao , Juyong Zhang , Bailin Deng

We propose a novel method to accelerate Lloyd's algorithm for K-Means clustering. Unlike previous acceleration approaches that reduce computational cost per iterations or improve initialization, our approach is focused on reducing the…

Machine Learning · Computer Science 2018-05-29 Juyong Zhang , Yuxin Yao , Yue Peng , Hao Yu , Bailin Deng

This paper investigates the use of fixed-point Anderson acceleration method (AA) to a recently proposed hierarchical control framework. Due to its model-free property, the AA-based resulting hierarchical framework becomes more generic since…

Systems and Control · Electrical Eng. & Systems 2021-12-09 Xuan-Huy Pham , Mazen Alamir , François Bonne , Patrick Bonnay

In this paper, we propose a novel Anderson's acceleration method to solve nonlinear equations, which does \emph{not} require a restart strategy to achieve numerical stability. We propose the greedy and random versions of our algorithm.…

Optimization and Control · Mathematics 2024-03-26 Haishan Ye , Dachao Lin , Xiangyu Chang , Zhihua Zhang

In the last few decades, several novel algorithms have been designed for finding critical points on PES and the minimum energy paths connecting them. This has led to considerably improve our understanding of reaction mechanisms and kinetics…

Computational Engineering, Finance, and Science · Computer Science 2024-10-30 Sandra Liz Simon , Nitin Kaistha , Vishal Agarwal

This paper studies the commonly utilized windowed Anderson acceleration (AA) algorithm for fixed-point methods, $x^{(k+1)}=q(x^{(k)})$. It provides the first proof that when the operator $q$ is linear and symmetric the windowed AA, which…

Numerical Analysis · Mathematics 2025-08-01 Casey Garner , Gilad Lerman , Teng Zhang

This work proposes a general strategy for solving possibly nonlinear problems arising from implicit time discretizations as a sequence of explicit solutions. The resulting sequence may exhibit instabilities similar to those of the base…

Numerical Analysis · Mathematics 2025-10-21 Nicolas A. Barnafi , Felipe Galarce , Pablo Brubeck

In this paper, we propose an Anderson-accelerated stochastic extragradient algorithm for solving a class of stochastic variational inequalities, by incorporating Anderson acceleration into the stochastic extragradient method under a…

Optimization and Control · Mathematics 2026-05-27 Xin Qu , Wei Bian , Xiaojun Chen

Anderson Acceleration (AA) has been widely used to solve nonlinear fixed-point problems due to its rapid convergence. This work focuses on a variant of AA in which multiple Picard iterations are performed between each AA step, referred to…

Numerical Analysis · Mathematics 2025-07-15 Xue Feng , M. Paul Laiu , Thomas Strohmer

We give a complete characterization of the behavior of the Anderson acceleration (with arbitrary nonzero mixing parameters) on linear problems. Let n be the grade of the residual at the starting point with respect to the matrix defining the…

Numerical Analysis · Mathematics 2011-02-07 Florian Potra , Hans Engler

Anderson mixing (AM) is a classical method that can accelerate fixed-point iterations by exploring historical information. Despite the successful application of AM in scientific computing, the theoretical properties of AM are still under…

Numerical Analysis · Mathematics 2023-07-06 Fuchao Wei , Chenglong Bao , Yang Liu , Guangwen Yang

The Uzawa algorithm is an iterative method for the solution of saddle-point problems, which arise in many applications, including fluid dynamics. Viewing the Uzawa algorithm as a fixed- point iteration, we explore the use of Anderson…

Numerical Analysis · Mathematics 2016-05-24 Nguyenho Ho , Sarah D. Olson , Homer F. Walker

This paper proposes an accelerated version of Feasible Sequential Linear Programming (FSLP): the AA($d$)-FSLP algorithm. FSLP preserves feasibility in all intermediate iterates by means of an iterative update strategy which is based on…

Optimization and Control · Mathematics 2024-07-08 David Kiessling , Pieter Pas , Alejandro Astudillo , Panagiotis Patrinos , Jan Swevers

We present a convergence theory for Anderson acceleration (AA) applied to perturbed Newton methods (pNMs) for computing roots of nonlinear problems. Two important special cases are the classical Newton method and the Levenberg-Marquardt…

Numerical Analysis · Mathematics 2025-12-03 Matt Dallas

This paper considers the numerical solution of generalized Sylvester matrix equations, which arise in many scientific and engineering applications but remain challenging to solve efficiently, particularly when the coefficient matrices are…

Numerical Analysis · Mathematics 2026-04-20 Hongjia Chen , Chun-Hua Zhang , Zhongming Teng , Lei Du

Partially observable Markov decision processes (POMDPs) is a rich mathematical framework that embraces a large class of complex sequential decision-making problems under uncertainty with limited observations. However, the complexity of…

Systems and Control · Electrical Eng. & Systems 2022-11-29 Mingyu Park , Jaeuk Shin , Insoon Yang

Alternating gradient-descent-ascent (AltGDA) is an optimization algorithm that has been widely used for model training in various machine learning applications, which aims to solve a nonconvex minimax optimization problem. However, the…

Machine Learning · Computer Science 2022-05-23 Ziyi Chen , Shaocong Ma , Yi Zhou

This paper presents a novel accelerated distributed algorithm for unconstrained consensus optimization over static undirected networks. The proposed algorithm combines the benefits of acceleration from momentum, the robustness of the…

Optimization and Control · Mathematics 2024-05-15 Eduardo Sebastián , Mauro Franceschelli , Andrea Gasparri , Eduardo Montijano , Carlos Sagüés