Global convergence of the Heavy-ball method for convex optimization
Optimization and Control
2014-12-24 v1
Abstract
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 where k is the number of iterations. When the objective function is also strongly convex, we prove that the Heavy-ball iterates converge linearly to the unique optimum.
Keywords
Cite
@article{arxiv.1412.7457,
title = {Global convergence of the Heavy-ball method for convex optimization},
author = {Euhanna Ghadimi and Hamid Reza Feyzmahdavian and Mikael Johansson},
journal= {arXiv preprint arXiv:1412.7457},
year = {2014}
}