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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

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

We consider the application of the type-I Anderson acceleration to solving general non-smooth fixed-point problems. By interleaving with safe-guarding steps, and employing a Powell-type regularization and a re-start checking for strong…

Optimization and Control · Mathematics 2018-08-14 Junzi Zhang , Brendan O'Donoghue , Stephen Boyd

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

We consider the solution of linear saddle-point problems, using the alternating direction method-of-multipliers (ADMM) as a preconditioner for the generalized minimum residual method (GMRES). We show, using theoretical bounds and empirical…

Optimization and Control · Mathematics 2016-04-28 Richard Y. Zhang , Jacob K. White

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

Model-free deep reinforcement learning (RL) algorithms have been widely used for a range of complex control tasks. However, slow convergence and sample inefficiency remain challenging problems in RL, especially when handling continuous and…

Machine Learning · Computer Science 2021-12-07 Wenjie Shi , Shiji Song , Hui Wu , Ya-Chu Hsu , Cheng Wu , Gao Huang

This paper proposes an accelerated method for approximately solving partially observable Markov decision process (POMDP) problems offline. Our method carefully combines two existing tools: Anderson acceleration (AA) and the fast informed…

Systems and Control · Electrical Eng. & Systems 2021-03-30 Melike Ermis , Mingyu Park , Insoon Yang

This paper proposes a new framework for computing low-rank solutions to nonlinear matrix equations arising from spatial discretization of nonlinear partial differential equations: low-rank Anderson acceleration (lrAA). lrAA is an adaptation…

Numerical Analysis · Mathematics 2025-03-25 Daniel Appelo , Yingda Cheng

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

Iteratively reweighted L1 (IRL1) algorithm is a common algorithm for solving sparse optimization problems with nonconvex and nonsmooth regularization. The development of its acceleration algorithm, often employing Nesterov acceleration, has…

Optimization and Control · Mathematics 2024-03-13 Kexin Li

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

Fixed-point solvers are ubiquitous in nonlinear PDEs, yet their progress collapses whenever the Jacobian at the solution carries an eigenvalue arbitrarily close to one. We ask whether such stagnation can be removed without storing long…

Numerical Analysis · Mathematics 2026-01-06 Francesco Alemanno

We propose an acceleration scheme for first-order methods (FOMs) for convex quadratic programs (QPs) that is analogous to Anderson acceleration and the Generalized Minimal Residual algorithm for linear systems. We motivate our proposed…

Optimization and Control · Mathematics 2026-04-09 Gabriel Berk Pereira , Paul J. Goulart

A pervasive approach in scientific computing is to express the solution to a given problem as the limit of a sequence of vectors or other mathematical objects. In many situations these sequences are generated by slowly converging iterative…

Numerical Analysis · Mathematics 2025-07-17 Yousef Saad

We consider the sequence acceleration problem for the alternating direction method-of-multipliers (ADMM) applied to a class of equality-constrained problems with strongly convex quadratic objectives, which frequently arise as the Newton…

Optimization and Control · Mathematics 2020-04-28 Richard Y. Zhang , Jacob K. White

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

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

Many scientific applications require the evaluation of the action of the matrix function over a vector and the most common methods for this task are those based on the Krylov subspace. Since the orthogonalization cost and memory requirement…

Numerical Analysis · Mathematics 2026-03-24 Nicolas L. Guidotti , Per-Gunnar Martinsson , Juan A. Acebrón , José Monteiro

Many computer graphics problems require computing geometric shapes subject to certain constraints. This often results in non-linear and non-convex optimization problems with globally coupled variables, which pose great challenge for…

Graphics · Computer Science 2018-05-16 Yue Peng , Bailin Deng , Juyong Zhang , Fanyu Geng , Wenjie Qin , Ligang Liu