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Recently Grimmer [1] showed for smooth convex optimization by utilizing longer steps periodically, gradient descent's textbook $LD^2/2T$ convergence guarantees can be improved by constant factors, conjecturing an accelerated rate strictly faster than $O(1/T)$ could be possible.
On richardson’s method for solving linear systems with positive definite matrices
David Young · 1953
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Performance of first-order methods for smooth convex minimization: a novel approach
Yoel Drori and Marc Teboulle · 2012
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Introductory Lectures on Convex Optimization: A Basic Course
Yurii Nesterov · 2014
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Olivier Devolder, François Glineur, and Yurii Nesterov · 2014
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Dimitri P. Bertsekas · 2015
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Cyclical learning rates for training neural networks
Leslie N. Smith · 2015
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Adrien Taylor, Julien Hendrickx, and François Glineur · 2017
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Super-convergence: very fast training of neural networks using large learning rates
Leslie N. Smith and Nicholay Topin · 2017
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Adrien Taylor, Julien Hendrickx, and François Glineur · 2017
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The exact worst-case convergence rate of the gradient method with fixed step lengths for l-smooth functions
An elementary approach to tight worst case complexity analysis of gradient based methods
Marc Teboulle and Yakov Vaisbourd · 2022
Later among the works it cites.
Provably Faster Gradient Descent via Long Steps
B. Grimmer · 2023
Closest in time.
Branch-and-bound performance estimation programming: A unified methodology for constructing optimal optimization methods
Shuvomoy Das Gupta, Bart P.G. Van Parys, and Ernest Ryu · 2023
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Acceleration by stepsize hedging i: Multi-step descent and the silver stepsize schedule, 2023
Jason M. Altschuler and Pablo A. Parrilo · 2023
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Mathematica, Version 13.3
Wolfram Research, Inc · 2023
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Hadi Abbaszadehpeivasti, Etienne de Klerk, and Moslem Zamani · 2021
Cited alongside, same era.