The exact worst-case convergence rate of the gradient method with fixed step lengths for L-smooth functions
Optimization and Control
2021-10-08 v3
Abstract
In this paper, we study the convergence rate of the gradient (or steepest descent) method with fixed step lengths for finding a stationary point of an -smooth function. We establish a new convergence rate, and show that the bound may be exact in some cases, in particular when all step lengths lie in the interval . In addition, we derive an optimal step length with respect to the new bound.
Keywords
Cite
@article{arxiv.2104.05468,
title = {The exact worst-case convergence rate of the gradient method with fixed step lengths for L-smooth functions},
author = {Hadi Abbaszadehpeivasti and Etienne de Klerk and Moslem Zamani},
journal= {arXiv preprint arXiv:2104.05468},
year = {2021}
}