English

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 LL-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 (0,1/L](0,1/L]. 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}
}