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The alternating direction method of multipliers (ADMM) is a popular approach for solving optimization problems that are potentially non-smooth and with hard constraints. It has been applied to various computer graphics applications,…

Graphics · Computer Science 2019-09-04 Juyong Zhang , Yue Peng , Wenqing Ouyang , Bailin Deng

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

Anderson mixing (AM) is an acceleration method for fixed-point iterations. Despite its success and wide usage in scientific computing, the convergence theory of AM remains unclear, and its applications to machine learning problems are not…

Machine Learning · Computer Science 2021-10-05 Fuchao Wei , Chenglong Bao , Yang Liu

This work investigates the local convergence behavior of Anderson acceleration in solving nonlinear systems. We establish local R-linear convergence results for Anderson acceleration with general depth $m$ under the assumptions that the…

Numerical Analysis · Mathematics 2025-07-22 Yonghui Ling , Zikang Xiong , Juan Liang

Multilinear systems play an important role in scientific calculations of practical problems. In this paper, we consider a tensor splitting method with a relaxed Anderson acceleration for solving multilinear systems. The new method preserves…

Numerical Analysis · Mathematics 2024-10-18 Dongdong Liu Ting Hua nd Xifu Liu

This paper develops an efficient and robust solution technique for the steady Boussinesq model of non-isothermal flow using Anderson acceleration applied to a Picard iteration. After analyzing the fixed point operator associated with the…

Numerical Analysis · Mathematics 2020-04-15 Sara Pollock , Leo G. Rebholz , Mengying Xiao

Despite their frequent slow convergence, proximal gradient schemes are widely used in large-scale optimization tasks due to their tremendous stability, scalability, and ease of computation. In this paper, we develop and investigate a…

Computation · Statistics 2025-08-19 Nicholas C. Henderson , Ravi Varadhan

In this paper we develop convergence and acceleration theory for Anderson acceleration applied to Newton's method for nonlinear systems in which the Jacobian is singular at a solution. For these problems, the standard Newton algorithm…

Numerical Analysis · Mathematics 2023-10-27 Matt Dallas , Sara Pollock

Anderson acceleration (AA) has a long history of use and a strong recent interest due to its potential ability to dramatically improve the linear convergence of the fixed-point iteration. Most authors are simply using and analyzing the…

Numerical Analysis · Mathematics 2022-02-14 Kewang Chen , Cornelis Vuik

Anderson acceleration (AA) is a popular method for accelerating fixed-point iterations, but may suffer from instability and stagnation. We propose a globalization method for AA to improve stability and achieve unified global and local…

Optimization and Control · Mathematics 2023-05-03 Wenqing Ouyang , Jiong Tao , Andre Milzarek , Bailin Deng

This paper studies a finite element discretization of the regularized Bingham equations that describe viscoplastic flow. An efficient nonlinear solver for the discrete model is then proposed and analyzed. The solver is based on Anderson…

Numerical Analysis · Mathematics 2022-12-09 Sara Pollock , Leo G. Rebholz , Duygu Vargun

This paper provides the first proof that Anderson acceleration (AA) improves the convergence rate of general fixed point iterations. AA has been used for decades to speed up nonlinear solvers in many applications, however a rigorous…

Numerical Analysis · Mathematics 2019-02-22 Claire Evans , Sara Pollock , Leo G. Rebholz , Mengying Xiao

In this paper, we study the local linear convergence properties of a versatile class of Primal-Dual splitting methods for minimizing composite non-smooth convex optimization problems. Under the assumption that the non-smooth components of…

Optimization and Control · Mathematics 2018-01-10 Jingwei Liang , Jalal Fadili , Gabriel Peyré

The expectation-maximization (EM) algorithm is a well-known iterative method for computing maximum likelihood estimates from incomplete data. Despite its numerous advantages, a main drawback of the EM algorithm is its frequently observed…

Computation · Statistics 2018-08-14 Nicholas C. Henderson , Ravi Varadhan

This paper proposes an extra gradient Anderson-accelerated algorithm for solving pseudomonotone variational inequalities, which uses the extra gradient scheme with line search to guarantee the global convergence and Anderson acceleration to…

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

In this paper, we study the robust linearization of nonlinear poromechanics of unsaturated materials. The model of interest couples the Richards equation with linear elasticity equations, employing the equivalent pore pressure. In practice…

Numerical Analysis · Mathematics 2021-05-24 Jakub Wiktor Both , Kundan Kumar , Jan Martin Nordbotten , Florin Adrian Radu

We consider nonlinear convergence acceleration methods for fixed-point iteration $x_{k+1}=q(x_k)$, including Anderson acceleration (AA), nonlinear GMRES (NGMRES), and Nesterov-type acceleration (corresponding to AA with window size one). We…

Optimization and Control · Mathematics 2020-11-10 Hans De Sterck , Yunhui He

Anderson Acceleration is a well-established method that allows to speed up or encourage convergence of fixed-point iterations. It has been successfully used in a variety of applications, in particular within the Self-Consistent Field (SCF)…

Numerical Analysis · Mathematics 2024-10-08 Ning Wan , Agnieszka Międlar

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 paper we consider the neural network optimization. We develop Anderson-type acceleration method for the stochastic gradient decent method and it improves the network permanence very much. We demonstrate the applicability of the…

Numerical Analysis · Mathematics 2025-12-11 Kazufumi Ito , Tiancheng Xue