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Although Anderson acceleration (AA) is known to speed up fixed-point iterations, it is rarely applied in constrained optimization, in particular sequential quadratic programming (SQP). We show that the local convergence behavior of a…

Optimization and Control · Mathematics 2026-04-17 Jonathan Frey , David Kiessling , Katrin Baumgärtner , Moritz Diehl

This paper can be seen as an attempt of rethinking the {\em Extra-Gradient Philosophy} for solving Variational Inequality Problems. We show that the properly defined {\em Reduced Gradients} can be used instead for finding approximate…

Optimization and Control · Mathematics 2023-12-05 Yurii Nesterov

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

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

This paper applies the Anderson Acceleration (AA) technique to accelerate the Fenchel dual gradient method (FDGM) to solve constrained optimization problems over time-varying networks. AA is originally designed for accelerating fixed-point…

Optimization and Control · Mathematics 2026-01-21 Haijuan Liu , Xuyang Wu

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

In this paper we study the pseudomonotone equilibrium problem. We consider a new inertial condition for the subgradient extragradient method with self-adaptive step size for approximating a solution of the equilibrium problem in a real…

Optimization and Control · Mathematics 2023-11-01 Chinedu Izuchukwu , Grace Ogwo , Bertin Zinsou

We consider stochastic variational inequality problems where the mapping is monotone over a compact convex set. We present two robust variants of stochastic extragradient algorithms for solving such problems. Of these, the first scheme…

Optimization and Control · Mathematics 2014-03-25 Farzad Yousefian , Angelia Nedic , Uday V. Shanbhag

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 consider the Anderson acceleration method for solving the contractive fixed point problem, which is nonsmooth in general. We define a class of smoothing functions for the original nonsmooth fixed point mapping, which can…

Optimization and Control · Mathematics 2024-12-11 Zekai Li , Wei Bian

We consider the problem of non-smooth convex optimization with linear equality constraints, where the objective function is only accessible through its proximal operator. This problem arises in many different fields such as statistical…

Optimization and Control · Mathematics 2020-11-18 Anqi Fu , Junzi Zhang , 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

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

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

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

The paper investigates two inertial extragradient algorithms for seeking a common solution to a variational inequality problem involving a monotone and Lipschitz continuous mapping and a fixed point problem with a demicontractive mapping in…

Optimization and Control · Mathematics 2023-08-08 Bing Tan , Liya Liu , Xiaolong Qin

We provide rigorous theoretical bounds for Anderson acceleration (AA) that allow for approximate calculations when applied to solve linear problems. We show that, when the approximate calculations satisfy the provided error bounds, the…

Numerical Analysis · Mathematics 2024-04-30 Massimiliano Lupo Pasini , M. Paul Laiu

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

Gradient descent algorithms perform well in convex optimization but can get tied for finding local minima in non-convex optimization. A robust method that combines a spectral approach with nonmonotone line search strategy for solving…

Optimization and Control · Mathematics 2025-01-07 Oday Hazaimah

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