English
Related papers

Related papers: Convergence Acceleration of Preconditioned CG Solv…

200 papers

In this paper, we propose a randomized accelerated method for the minimization of a strongly convex function under linear constraints. The method is of Kaczmarz-type, i.e. it only uses a single linear equation in each iteration. To obtain…

Optimization and Control · Mathematics 2025-04-03 Lionel Tondji , Dirk A. Lorenz , Ion Necoara

This work is concerned with approximating the smallest eigenvalue of a parameter-dependent Hermitian matrix $A(\mu)$ for many parameter values $\mu \in \mathbb{R}^P$. The design of reliable and efficient algorithms for addressing this task…

Numerical Analysis · Mathematics 2015-04-24 Petar Sirković , Daniel Kressner

We establish a new iterative method for solving a class of large and sparse linear systems of equations with three-by-three block coefficient matrices having saddle point structure. Convergence properties of the proposed method are studied…

Numerical Analysis · Mathematics 2021-09-13 Hamed Aslani , Davod Khojasteh Salkuyeh , Fatemeh Panjeh Ali Beik

Efficient numerical solvers for partial differential equations empower science and engineering. One of the commonly employed numerical solvers is the preconditioned conjugate gradient (PCG) algorithm which can solve large systems to a given…

Numerical Analysis · Mathematics 2023-09-07 Yichen Li , Peter Yichen Chen , Tao Du , Wojciech Matusik

This paper introduces a preconditioned method designed to comprehensively address the saddle point system with the aim of improving convergence efficiency. In the preprocessor construction phase, a technical approach for solving the…

Numerical Analysis · Mathematics 2024-04-10 Juan Zhang , Yiyi Luo

We propose a variant of the classical conditional gradient method for sparse inverse problems with differentiable measurement models. Such models arise in many practical problems including superresolution, time-series modeling, and matrix…

Optimization and Control · Mathematics 2015-07-07 Nicholas Boyd , Geoffrey Schiebinger , Benjamin Recht

The conjugate gradient solver (CG) is a prevalent method for solving symmetric and positive definite linear systems Ax=b, where effective preconditioners are crucial for fast convergence. Traditional preconditioners rely on prescribed…

Machine Learning · Computer Science 2025-11-03 Zherui Yang , Zhehao Li , Kangbo Lyu , Yixuan Li , Tao Du , Ligang Liu

In this paper, we propose a descent method for composite optimization problems with linear operators. Specifically, we first design a structure-exploiting preconditioner tailored to the linear operator so that the resulting preconditioned…

Optimization and Control · Mathematics 2026-03-20 Jian Chen , Xinmin Yang

Composite optimization problems involve minimizing the composition of a smooth map with a convex function. Such objectives arise in numerous data science and signal processing applications, including phase retrieval, blind deconvolution,…

Optimization and Control · Mathematics 2025-10-06 Mateo Díaz , Liwei Jiang , Abdel Ghani Labassi

This paper introduces the multiplicative variant of the recently proposed asynchronous additive coarse-space correction method. Definition of an asynchronous extension of multiplicative correction is not straightforward, however, our…

Numerical Analysis · Mathematics 2023-12-20 Guillaume Gbikpi-Benissan , Frédéric Magoulès

Atmospheric powered descent guidance can be solved by successive convexification; however, its onboard application is impeded by the sharp increase in computation caused by nonlinear aerodynamic forces. The problem has to be converted into…

Systems and Control · Electrical Eng. & Systems 2023-06-07 Yushu Chen , Guangwen Yang , Lu Wang , Qingzhong Gan , Haipeng Chen , Quanyong Xu

Subspace recycling techniques have been used quite successfully for the acceleration of iterative methods for solving large-scale linear systems. These methods often work by augmenting a solution subspace generated iteratively by a known…

Numerical Analysis · Mathematics 2021-05-18 Ronny Ramlau , Kirk M. Soodhalter , Victoria Hutterer

The problem of low-tubal-rank tensor estimation is a fundamental task with wide applications across high-dimensional signal processing, machine learning, and image science. Traditional approaches tackle such a problem by performing tensor…

Machine Learning · Computer Science 2025-12-24 Zhiyu Liu , Zhi Han , Yandong Tang , Jun Fan , Yao Wang

This paper addresses the bilinearly coupled minimax optimization problem: $\min_{x \in \mathbb{R}^{d_x}}\max_{y \in \mathbb{R}^{d_y}} \ f_1(x) + f_2(x) + y^{\top} Bx - g_1(y) - g_2(y)$, where $f_1$ and $g_1$ are smooth convex functions,…

Optimization and Control · Mathematics 2025-05-27 Jingwang Li , Xiao Li

The method of alternation projections (MAP) is an iterative procedure for finding the projection of a point on the intersection of closed subspaces of an Hilbert space. The convergence of this method is usually slow, and several methods for…

Numerical Analysis · Mathematics 2013-02-04 Claude Brezinski , Michela Redivo-Zaglia

There has been a growing interest in parallel strategies for solving trajectory optimization problems. One key step in many algorithmic approaches to trajectory optimization is the solution of moderately-large and sparse linear systems.…

Optimization and Control · Mathematics 2024-03-05 Xueyi Bu , Brian Plancher

Discrete optimization belongs to the set of $\mathcal{NP}$-hard problems, spanning fields such as mixed-integer programming and combinatorial optimization. A current standard approach to solving convex discrete optimization problems is the…

Machine Learning · Computer Science 2024-02-28 Kyle Mana , Fernando Acero , Stephen Mak , Parisa Zehtabi , Michael Cashmore , Daniele Magazzeni , Manuela Veloso

In recent years, the fervent demand for computational power across various domains has prompted hardware manufacturers to introduce specialized computing hardware aimed at enhancing computational capabilities. Particularly, the utilization…

Numerical Analysis · Mathematics 2024-03-12 Hongyaoxing Gu

An adapted deflation preconditioner is employed to accelerate the solution of linear systems resulting from the discretization of fracture mechanics problems with well-conditioned extended/generalized finite elements. The deflation space…

Computational Engineering, Finance, and Science · Computer Science 2022-05-11 Konstantinos Agathos , Tim Dodwell , Eleni Chatzi , Stephane P. A. Bordas

We propose an adaptive accelerated gradient method for solving smooth convex optimization problems. The method incorporates a scheme to determine the step size adaptively, by means of a local estimation of the smoothness constant, which is…

Optimization and Control · Mathematics 2025-12-24 Zepeng Wang , Juan Peypouquet