Related papers: A cooperative conjugate gradient method for linear…
The standard implementation of the conjugate gradient algorithm suffers from communication bottlenecks on parallel architectures, due primarily to the two global reductions required every iteration. In this paper, we study conjugate…
In recent years, topology optimization has been developed sufficiently and many researchers have concentrated on enhancing to computationally numerical algorithms for computational effectiveness of this method. Along with the development of…
In [Meurant, Pape\v{z}, Tich\'y; Numerical Algorithms 88, 2021], we presented an adaptive estimate for the energy norm of the error in the conjugate gradient (CG) method. In this paper, we extend the estimate to algorithms for solving…
Nonlinear conjugate gradients are among the most popular techniques for solving continuous optimization problems. Although these schemes have long been studied from a global convergence standpoint, their worst-case complexity properties…
Data-driven iterative learning control can achieve high performance for systems performing repeating tasks without the need for modeling. The aim of this paper is to develop a fast data-driven method for iterative learning control that is…
Gradient tracking methods have emerged as one of the most popular approaches for solving decentralized optimization problems over networks. In this setting, each node in the network has a portion of the global objective function, and the…
This study concerns the fast and accurate solution of the line radiation transfer problem, under non-LTE conditions. We propose and evaluate an alternative iterative scheme to the classical ALI-Jacobi method, and to the more recently…
In this paper, we present a conditional gradient type (CGT) method for solving a class of composite optimization problems where the objective function consists of a (weakly) smooth term and a (strongly) convex regularization term. While…
In the book [Meurant and Tichy, SIAM, 2024] we discussed the estimation of error norms in the conjugate gradient (CG) algorithm for solving linear systems $Ax=b$ with a symmetric positive definite matrix $A$, where $b$ and $x$ are vectors.…
A coarse grid correction (CGC) approach is proposed to enhance the efficiency of the matrix exponential and $\varphi$ matrix function evaluations. The approach is intended for iterative methods computing the matrix-vector products with…
This work studies gradient coding (GC) in the context of distributed training problems with unreliable communication. We propose cooperative GC (CoGC), a novel gradient-sharing-based GC framework that leverages cooperative communication…
As compared to using randomly generated sensing matrices, optimizing the sensing matrix w.r.t. a carefully designed criterion is known to lead to better quality signal recovery given a set of compressive measurements. In this paper, we…
The purpose of this paper is to introduce two new classes of accelerated distributed proximal conjugate gradient algorithms for multi-agent constrained optimization problems; given as minimization of a function decomposed as a sum of M…
We propose a gradient-based method for quadratic programming problems with a single linear constraint and bounds on the variables. Inspired by the GPCG algorithm for bound-constrained convex quadratic programming [J.J. Mor\'e and G.…
In this paper, we consider the conjugate gradient method for solving the problem of minimizing a quadratic function with additive noise in the gradient. Three concepts of noise were considered: antagonistic noise in the linear term,…
In this paper, we propose a new non-monotone conjugate gradient method for solving unconstrained nonlinear optimization problems. We first modify the non-monotone line search method by introducing a new trigonometric function to calculate…
We explore a scaled spectral preconditioner for the efficient solution of sequences of symmetric and positive-definite linear systems. We design the scaled preconditioner not only as an approximation of the inverse of the linear system but…
We consider three mathematically equivalent variants of the conjugate gradient (CG) algorithm and how they perform in finite precision arithmetic. It was shown in [{\em Behavior of slightly perturbed Lanczos and conjugate-gradient…
Nesterov's accelerated gradient method for minimizing a smooth strongly convex function $f$ is known to reduce $f(\x_k)-f(\x^*)$ by a factor of $\eps\in(0,1)$ after $k\ge O(\sqrt{L/\ell}\log(1/\eps))$ iterations, where $\ell,L$ are the two…
The recent article "A Bayesian conjugate gradient method" by Cockayne, Oates, Ipsen, and Girolami proposes an approximately Bayesian iterative procedure for the solution of a system of linear equations, based on the conjugate gradient…