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

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...

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Vydané v:	Optimization letters Ročník 16; číslo 6; s. 1649 - 1661
Hlavní autori:	Abbaszadehpeivasti, Hadi, de Klerk, Etienne, Zamani, Moslem
Médium:	Journal Article
Jazyk:	English
Vydavateľské údaje:	Berlin/Heidelberg Springer Berlin Heidelberg 01.07.2022
Predmet:	Computational Intelligence Mathematics Mathematics and Statistics Numerical and Computational Physics Operations Research/Decision Theory Optimization Original Paper Simulation smooth optimization Performance estimation problem Semidefinite programming Gradient method
ISSN:	1862-4472, 1862-4480
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Popis
Shrnutí:	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.
ISSN:	1862-4472 1862-4480
DOI:	10.1007/s11590-021-01821-1