The exact worst-case convergence rate of the gradient method with fixed step lengths for L-smooth functions

Hadi Abbaszadehpeivasti, Etienne de Klerk, Moslem Zamani*

*Corresponding author for this work

Research output: Contribution to journalArticleScientificpeer-review

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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 L-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]. In addition, we derive an optimal step length with respect to the new bound.
Original languageEnglish
JournalOptimization Letters
DOIs
Publication statusE-pub ahead of print - Nov 2021

Keywords

  • l-smooth optimization
  • gradient method
  • performance estomation prolem
  • semidefinite programming

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