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Related papers: Convergence of Constrained Anderson Acceleration

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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

Nesterov's well-known scheme for accelerating gradient descent in convex optimization problems is adapted to accelerating stationary iterative solvers for linear systems. Compared with classical Krylov subspace acceleration methods, the…

Optimization and Control · Mathematics 2021-08-10 Tao Hong , Irad Yavneh

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

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

Anderson acceleration is an effective technique for enhancing the efficiency of fixed-point iterations; however, analyzing its convergence in nonsmooth settings presents significant challenges. In this paper, we investigate a class of…

Optimization and Control · Mathematics 2024-10-16 Kexin Li , Luwei Bai , Xiao Wang , Hao Wang

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 exploit analogies between first-order algorithms for constrained optimization and non-smooth dynamical systems to design a new class of accelerated first-order algorithms for constrained optimization. Unlike Frank-Wolfe or projected…

Optimization and Control · Mathematics 2025-05-02 Michael Muehlebach , Michael I. Jordan

Anderson acceleration (AA) is widely used for accelerating the convergence of an underlying fixed-point iteration $\bm{x}_{k+1} = \bm{q}( \bm{x}_{k} )$, $k = 0, 1, \ldots$, with $\bm{x}_k \in \mathbb{R}^n$, $\bm{q} \colon \mathbb{R}^n \to…

Numerical Analysis · Mathematics 2025-05-14 Oliver A. Krzysik , Hans De Sterck , Adam Smith

This work proposes an accelerated primal-dual dynamical system for affine constrained convex optimization and presents a class of primal-dual methods with nonergodic convergence rates. In continuous level, exponential decay of a novel…

Optimization and Control · Mathematics 2022-04-12 Hao Luo

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

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

A one-step analysis of Anderson acceleration with general algorithmic depths is presented. The resulting residual bounds within both contractive and noncontractive settings reveal the balance between the contributions from the higher and…

Numerical Analysis · Mathematics 2022-09-08 Sara Pollock , Leo Rebholz

We show that Nesterov acceleration is an optimal-order iterative regularization method for linear ill-posed problems provided that a parameter is chosen accordingly to the smoothness of the solution. This result is proven both for an a…

Numerical Analysis · Mathematics 2021-07-07 Stefan Kindermann

We prove new convergence rates for a generalized version of stochastic Nesterov acceleration under interpolation conditions. Unlike previous analyses, our approach accelerates any stochastic gradient method which makes sufficient progress…

Optimization and Control · Mathematics 2025-01-27 Aaron Mishkin , Mert Pilanci , Mark Schmidt

Efficient solvers for tensor eigenvalue problems are important tools for the analysis of higher-order data sets. Here we introduce, analyze and demonstrate an extrapolation method to accelerate the widely used shifted symmetric higher order…

Numerical Analysis · Mathematics 2023-07-25 Sara Pollock , Rhea Shroff

We consider a class of multi-agent cooperative consensus optimization problems with local nonlinear convex constraints where only those agents connected by an edge can directly communicate, hence, the optimal consensus decision lies in the…

Optimization and Control · Mathematics 2023-02-23 Nazanin Abolfazli , Afrooz Jalilzadeh , Erfan Yazdandoost Hamedani

Convergence rates are established for an inexact accelerated alternating direction method of multipliers (I-ADMM) for general separable convex optimization with a linear constraint. Both ergodic and non-ergodic iterates are analyzed.…

Numerical Analysis · Mathematics 2021-07-20 William W. Hager , Hongchao Zhang

We study the convergence rate of Sinkhorn's algorithm for solving entropy-regularized optimal transport problems when at least one of the probability measures, $\mu$, admits a density over $\mathbb{R}^d$. For a semi-concave cost function…

Optimization and Control · Mathematics 2025-07-21 Lénaïc Chizat , Alex Delalande , Tomas Vaškevičius

In this paper, we consider nonconvex optimization problems with nonsmooth nonconvex objective function and nonlinear equality constraints. We assume that both the objective function and the functional constraints can be separated into 2…

Optimization and Control · Mathematics 2025-03-04 Lahcen El Bourkhissi , Ion Necoara

For a class of finite elements approximations for linear stochastic parabolic PDEs it is proved that one can accelerate the rate of convergence by Richardson extrapolation. More precisely, by taking appropriate mixtures of finite elements…

Probability · Mathematics 2022-10-11 István Gyöngy , Annie Millet