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This work establishes new convergence guarantees for gradient descent in smooth convex optimization via a computer-assisted analysis technique.
On richardson’s method for solving linear systems with positive definite matrices
David Young · 1953
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Ordering of the iterative parameters in the cyclical chebyshev iterative method
V.I. Lebedev and S.A. Finogenov · 1971
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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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Contributions to the complexity analysis of optimization algorithms
Yoel Drori · 2014
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Convex optimization algorithms
Dimitri P. Bertsekas · 2015
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Cyclical learning rates for training neural networks
Leslie N. Smith · 2015
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On the worst-case complexity of the gradient method with exact line search for smooth strongly convex functions
Etienne de Klerk, François Glineur, and Adrien Taylor · 2016
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Optimized first-order methods for smooth convex minimization
Donghwan Kim and Jeffrey A. Fessler · 2016
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Sgdr: Stochastic gradient descent with restarts
Ilya Loshchilov and Frank Hutter · 2016
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Spectra – a maple library for solving linear matrix inequalities in exact arithmetic
Didier Henrion, Simone Naldi, and Mohab Safey El Din · 2016
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Smooth strongly convex interpolation and exact worst-case performance of first-order methods
Adrien Taylor, Julien Hendrickx, and François Glineur · 2017
Earlier work this paper cites.
Exact worst-case performance of first-order methods for composite convex optimization
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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Greed, hedging, and acceleration in convex optimization
Jason Altschuler · 2018
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Lyapunov functions for first-order methods: Tight automated convergence guarantees
Adrien Taylor, Bryan Van Scoy, and Laurent Lessard · 2018
Cited alongside, same era.
Efficient first-order methods for convex minimization: a constructive approach
Yoel Drori and Adrien Taylor · 2018
Cited alongside, same era.
Optimal complexity and certification of bregman first-order methods
Radu-Alexandru Dragomir, Adrien Taylor, Alexandre d’Aspremont, and Jérôme Bolte · 2019
Cited alongside, same era.
Stochastic first-order methods: non-asymptotic and computer-aided analyses via potential functions
Adrien Taylor and Francis Bach · 2019
Cited alongside, same era.
Performance estimation of the gradient method with fixed arbitrary step sizes
Antoine Daccache · 2019
Cited alongside, same era.
An optimal-storage approach to semidefinite programming using approximate complementarity
Lijun Ding, Alp Yurtsever, Volkan Cevher, Joel A. Tropp, and Madeleine Udell · 2021
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Scalable semidefinite programming
Alp Yurtsever, Joel A. Tropp, Olivier Fercoq, Madeleine Udell, and Volkan Cevher · 2021
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Principled analyses and design of first-order methods with inexact proximal operators
Mathieu Barré, Adrien Taylor, and Francis Bach · 2022
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An optimal gradient method for smooth strongly convex minimization
Adrien Taylor and Yoel Drori · 2022
Later among the works it cites.
An elementary approach to tight worst case complexity analysis of gradient based methods
Marc Teboulle and Yakov Vaisbourd · 2022
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Worst-case functions for the gradient method with fixed variable step sizes
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A relaxed interior point method for low-rank semidefinite programming problems with applications to matrix completion
Stefania Bellavia, Jacek Gondzio, and Margherita Porcelli · 2019
Cited alongside, same era.
On the convergence rate of the halpern-iteration
Felix Lieder · 2020
Cited alongside, same era.
Operator splitting performance estimation: Tight contraction factors and optimal parameter selection
Ernest Ryu, Adrien Taylor, Carolina Bergeling, and Pontus Giselsson · 2020
Cited alongside, same era.
Tight sublinear convergence rate of the proximal point algorithm for maximal monotone inclusion problems
Guoyong Gu and Junfeng Yang · 2020
Cited alongside, same era.
Worst-case convergence analysis of inexact gradient and newton methods through semidefinite programming performance estimation
Etienne De Klerk, François Glineur, and Adrien B. Taylor · 2020
Cited alongside, same era.
Optimizing the efficiency of first-order methods for decreasing the gradient of smooth convex functions
Donghwan Kim and Jeffrey A. Fessler · 2021
Cited alongside, same era.
Accelerated proximal point method for maximally monotone operators
Donghwan Kim · 2021
Cited alongside, same era.
Diego Eloi · 2022
Later among the works it cites.
Super-acceleration with cyclical step-sizes
Baptiste Goujaud, Damien Scieur, Aymeric Dieuleveut, Adrien B. Taylor, and Fabian Pedregosa · 2022
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Exploiting low-rank structure in semidefinite programming by approximate operator splitting
Mario Souto, Joaquim D. Garcia, and Álvaro Veiga · 2022
Later among the works it cites.
Accelerated first-order methods for a class of semidefinite programs, 2022
Alex L. Wang and Fatma Kilinc-Karzan · 2022
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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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Optimal convergence rates for the proximal bundle method
Mateo Díaz and Benjamin Grimmer · 2023
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Computer-assisted design of accelerated composite optimization methods: Optista, 2023
Uijeong Jang, Shuvomoy Das Gupta, and Ernest K. Ryu · 2023
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Implicit regularity and linear convergence rates for the generalized trust-region subproblem
Alex L. Wang, Yunlei Lu, and Fatma Kilinç-Karzan · 2023
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Revisiting spectral bundle methods: Primal-dual (sub)linear convergence rates
Lijun Ding and Benjamin Grimmer · 2023
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