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We present theoretical results on the convergence of \emph{non-convex} accelerated gradient descent in matrix factorization models with $\ell_2$-norm loss. The purpose of this work is to study the effects of acceleration in non-convex…

Machine Learning · Computer Science 2019-09-24 Tayo Ajayi , David Mildebrath , Anastasios Kyrillidis , Shashanka Ubaru , Georgios Kollias , Kristofer Bouchard

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

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

Anderson acceleration (AA) is widely used for accelerating the convergence of nonlinear fixed-point methods $x_{k+1}=q(x_{k})$, $x_k \in \mathbb{R}^n$, but little is known about how to quantify the convergence acceleration provided by AA.…

Numerical Analysis · Mathematics 2023-02-27 Hans De Sterck , Yunhui He , Oliver A. Krzysik

In this paper, we propose and analyze a set of fully non-stationary Anderson acceleration algorithms with dynamic window sizes and optimized damping. Although Anderson acceleration (AA) has been used for decades to speed up nonlinear…

Numerical Analysis · Mathematics 2022-03-29 Kewang Chen , Cornelis Vuik

In this paper, by employing the asymptotic expansion method, we prove the existence and uniqueness of a smoothing solution for a time-dependent nonlinear singularly perturbed partial differential equation (PDE) with a small-scale parameter.…

Numerical Analysis · Mathematics 2022-10-11 Dmitrii Chaikovskii , Ye Zhang

This paper deals with a general class of algorithms for the solution of fixed-point problems that we refer to as \emph{Anderson--Pulay acceleration}. This family includes the DIIS technique and its variant sometimes called commutator-DIIS,…

Numerical Analysis · Mathematics 2021-11-19 Maxime Chupin , Mi-Song Dupuy , Guillaume Legendre , Eric Séré

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

Stochastic nonconvex optimization problems with nonlinear constraints have a broad range of applications in intelligent transportation, cyber-security, and smart grids. In this paper, first, we propose an inexact-proximal accelerated…

Optimization and Control · Mathematics 2021-07-08 Morteza Boroun , Afrooz Jalilzadeh

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

Recently, accelerated algorithms using the anchoring mechanism for minimax optimization and fixed-point problems have been proposed, and matching complexity lower bounds establish their optimality. In this work, we present the surprising…

Optimization and Control · Mathematics 2024-04-25 TaeHo Yoon , Jaeyeon Kim , Jaewook J. Suh , Ernest K. Ryu

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

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

We analyze the convergence rate of the monotone accelerated proximal gradient method, which can be used to solve structured convex composite optimization problems. A linear convergence rate is established when the smooth part of the…

Optimization and Control · Mathematics 2026-03-16 Zepeng Wang , Juan Peypouquet

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

We propose an Anderson Acceleration (AA) scheme for the adaptive Expectation-Maximization (EM) algorithm for unsupervised learning a finite mixture model from multivariate data (Figueiredo and Jain 2002). The proposed algorithm is able to…

Machine Learning · Computer Science 2020-09-29 Truong Nguyen , Guangye Chen , Luis Chacon

In this paper, we design an inertial accelerated primal-dual algorithm to address the convex-concave saddle point problem, which is formulated as $\min_{x}\max_{y} f(x) + \langle Kx, y \rangle - g(y)$. Remarkably, both functions $f$ and $g$…

Optimization and Control · Mathematics 2024-04-17 X. He , N. J. Huang , Y. P. Fang

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

This work introduces a moving anchor acceleration technique to extragradient algorithms for smooth structured minimax problems. The moving anchor is introduced as a generalization of the original algorithmic anchoring framework, i.e. the…

Optimization and Control · Mathematics 2025-06-03 James K. Alcala , Yat Tin Chow , Mahesh Sunkula

In [19], a general, inexact, efficient proximal quasi-Newton algorithm for composite optimization problems has been proposed and a sublinear global convergence rate has been established. In this paper, we analyze the convergence properties…

Numerical Analysis · Computer Science 2017-10-18 Hiva Ghanbari , Katya Scheinberg