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arXiv · 2104.05468

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
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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.

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Hadi Abbaszadehpeivasti, Etienne de Klerk, Moslem Zamani. 2021-04-12. The exact worst-case convergence rate of the gradient method with fixed step lengths for L-smooth functions. https://arxiv.org/abs/2104.05468

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