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Nesterov's accelerated gradient method for minimizing a smooth strongly convex function $f$ is known to reduce $f(\x_k)-f(\x^*)$ by a factor of $\eps\in(0,1)$ after $k\ge O(\sqrt{L/\ell}\log(1/\eps))$ iterations, where $\ell,L$ are the two parameters of smooth strong convexity.
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Magnus Rudolph Hestenes and Eduard Stiefel · 1952
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Function minimization by conjugate gradients
R. Fletcher and C. Reeves · 1964
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The conjugate gradient method for linear and nonlinear operator equations
James W Daniel · 1967
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E. Polak and G. Ribière · 1969
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A. S. Nemirovsky and D. B. Yudin · 1979
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Numerical Optimization, 2nd Edition
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Steepest descent and conjugate gradient methods with variable preconditioning
A. V. Knyazev and I. Lashuk · 2007
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Fundamentals of convex analysis
Jean-Baptiste Hiriart-Urruty and Claude Lemaréchal · 2012
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Krylov subspace methods: principles and analysis
J. Liesen and Z. Strakos · 2013
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On the relationship between conjugate gradient and optimal first-order methods for convex optimization
Sahar Karimi · 2014
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A geometric alternative to Nesterov’s accelerated gradient descent
S. Bubeck, Y. T. Lee, and Mohit Singh · 2015
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J. van den Eshof and G. Sleijpen · 2004
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