Results 1 to 10 of about 22,838 (152)

Heavy Ball Restarted CMRH Methods for Linear Systems [PDF]

Mathematical and Computational Applications, 2018
The restarted CMRH method (changing minimal residual method based on the Hessenberg process) using fewer operations and storage is an alternative method to the restarted generalized minimal residual method (GMRES) method for linear systems.
Zhongming Teng, Xuansheng Wang
doaj   +2 more sources

Non-monotone Behavior of the Heavy Ball Method [PDF]

Springer Proceedings in Mathematics and Statistics, 2020
We focus on the solutions of second-order stable linear difference equations and demonstrate that their behavior can be non-monotone and exhibit peak effects depending on initial conditions. The results are applied to the analysis of the accelerated unconstrained optimization method -- the Heavy Ball method.
Marina Danilova, Boris Polyak
exaly   +3 more sources

Convergence rates of the Heavy-Ball method under the Łojasiewicz property

Mathematical Programming, 2022
zbMATH Open Web Interface contents unavailable due to conflicting licenses.
Aude Rondepierre
exaly   +4 more sources

Convergence Rates of the Heavy Ball Method for Quasi-strongly Convex Optimization

SIAM Journal on Optimization, 2022
zbMATH Open Web Interface contents unavailable due to conflicting licenses.
Jean-François Aujol, Aude Rondepierre
exaly   +5 more sources

Global convergence of the Heavy-ball method for convex optimization [PDF]

2015 European Control Conference (ECC), 2015
This paper establishes global convergence and provides global bounds of the convergence rate of the Heavy-ball method for convex optimization problems. When the objective function has Lipschitz-continuous gradient, we show that the Cesaro average of the iterates converges to the optimum at a rate of $O(1/k)$ where k is the number of iterations.
Mikael Johansson, Hamid Reza Feyzmahdavian, Euhanna Ghadimi   +2 more
exaly   +4 more sources

A robust control approach to asymptotic optimality of the heavy ball method for optimization of quadratic functions

Automatica, 2023
Among first order optimization methods, Polyak's heavy ball method has long been known to guarantee the asymptotic rate of convergence matching Nesterov's lower bound for functions defined in an infinite-dimensional space. In this paper, we use results on the robust gain margin of linear uncertain feedback control systems to show that the heavy ball ...
Iman Shames, Ian Petersen
exaly   +6 more sources

Suppressing Heavy Metal Leaching through Ball Milling of Fly Ash

Energies, 2016
Ball milling is investigated as a method of reducing the leaching concentration (often termed stablilization) of heavy metals in municipal solid waste incineration (MSWI) fly ash. Three heavy metals (Cu, Cr, Pb) loose much of their solubility in leachate
Zhiliang Chen, Shengyong Lu, Qiongjing Mao, Alfons Buekens, Wei Chang, Xu Wang, Jianhua Yan   +6 more
doaj   +3 more sources

Local Convergence of the Heavy-Ball Method and iPiano for Non-convex Optimization [PDF]

Journal of Optimization Theory and Applications, 2018
A local convergence result for abstract descent methods is proved. The sequence of iterates is attracted by a local (or global) minimum, stays in its neighborhood and converges within this neighborhood. This result allows algorithms to exploit local properties of the objective function.
Peter Ochs
exaly   +5 more sources

An Adaptive Heavy Ball Method for Ill-Posed Inverse Problems

SIAM Journal on Imaging Sciences
In this paper we consider ill-posed inverse problems, both linear and nonlinear, by a heavy ball method in which a strongly convex regularization function is incorporated to detect the feature of the sought solution. We develop ideas on how to adaptively choose the step-sizes and the momentum coefficients to achieve acceleration over the Landweber-type
Qinian Jin, Qin Huang
exaly   +4 more sources

Convergence analysis of a stochastic heavy-ball method for linear ill-posed problems

Journal of Computational and Applied Mathematics
In this paper we consider a stochastic heavy-ball method for solving linear ill-posed inverse problems. With suitable choices of the step-sizes and the momentum coefficients, we establish the regularization property of the method under {\it a priori} selection of the stopping index and derive the rate of convergence under a benchmark source condition ...
Qinian Jin, Yanjun Liu
exaly   +4 more sources