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Related papers: Anderson Acceleration of Proximal Gradient Methods

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Anderson Acceleration (AA) is a popular algorithm designed to enhance the convergence of fixed-point iterations. In this paper, we introduce a variant of AA based on a Truncated Gram-Schmidt process (AATGS) which has a few advantages over…

Numerical Analysis · Mathematics 2024-07-17 Ziyuan Tang , Tianshi Xu , Huan He , Yousef Saad , Yuanzhe Xi

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

In this work, we extend a modified Anderson acceleration proposed in [Y. He, arXiv:2603.25983, 2026] to accelerate the Picard iteration for the Navier-Stokes equations. In this variant of Anderson acceleration, named AAg, the nonlinear…

Numerical Analysis · Mathematics 2026-05-19 Yunhui He , Leo Rebholz

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

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 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

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

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

Riemannian accelerated gradient methods have been well studied for smooth optimization, typically treating geodesically convex and geodesically strongly convex cases separately. However, their extension to nonsmooth problems on manifolds…

Optimization and Control · Mathematics 2025-09-29 Shuailing Feng , Yuhang Jiang , Wen Huang , Shihui Ying

This paper examines a number of extrapolation and acceleration methods, and introduces a few modifications of the standard Shanks transformation that deal with general sequences. One of the goals of the paper is to lay out a general…

Numerical Analysis · Mathematics 2021-07-09 Claude Brezinski , Stefano Cipolla , Michela Redivo-Zaglia , Yousef Saad

In this paper, we propose a proximal gradient method and an accelerated proximal gradient method for solving composite optimization problems, where the objective function is the sum of a smooth and a convex, possibly nonsmooth, function. We…

Optimization and Control · Mathematics 2025-07-22 Raghu Bollapragada , Shagun Gupta

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

Convex-nonconvex (CNC) regularization is a novel paradigm that employs a nonconvex penalty function while maintaining the convexity of the entire objective function. It has been successfully applied to problems in signal processing,…

Optimization and Control · Mathematics 2025-02-21 Qiang Heng , Xiaoqian Liu , Eric C. Chi

Acceleration of first order methods is mainly obtained via inertial techniques \`a la Nesterov, or via nonlinear extrapolation. The latter has known a recent surge of interest, with successful applications to gradient and proximal gradient…

Machine Learning · Statistics 2021-10-29 Quentin Bertrand , Mathurin Massias

BoostConv has been introduced in earlier works as an effective acceleration technique for nonlinear iterative processes and has been successfully employed in a variety of applications to enhance convergence rates or to compute unstable…

Numerical Analysis · Mathematics 2026-03-24 Vincenzo Citro , Davide Palitta

The Anderson Mixing (AM) method is a popular approach for accelerating fixed-point iterations by leveraging historical information from previous steps. In this paper, we introduce the Riemannian Anderson Mixing (RAM) method, an extension of…

Optimization and Control · Mathematics 2023-09-13 Zanyu Li , Chenglong Bao

Many modern machine learning algorithms such as generative adversarial networks (GANs) and adversarial training can be formulated as minimax optimization. Gradient descent ascent (GDA) is the most commonly used algorithm due to its…

Machine Learning · Computer Science 2022-07-01 Huan He , Shifan Zhao , Yuanzhe Xi , Joyce C Ho , Yousef Saad

Nonconvex optimization problems arise in different research fields and arouse lots of attention in signal processing, statistics and machine learning. In this work, we explore the accelerated proximal gradient method and some of its…

Optimization and Control · Mathematics 2017-12-05 Tsz Kit Lau , Yuan Yao

Despite the impressive numerical performance of the quasi-Newton and Anderson/nonlinear acceleration methods, their global convergence rates have remained elusive for over 50 years. This study addresses this long-standing issue by…

Optimization and Control · Mathematics 2023-11-16 Damien Scieur

In this paper, we propose a new algorithm to speed-up the convergence of accelerated proximal gradient (APG) methods. In order to minimize a convex function $f(\mathbf{x})$, our algorithm introduces a simple line search step after each…

Machine Learning · Statistics 2014-06-19 Ziming Zhang , Venkatesh Saligrama