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We study first-order optimization methods obtained by discretizing ordinary differential equations (ODEs) corresponding to Nesterov's accelerated gradient methods (NAGs) and Polyak's heavy-ball method.
Some methods of speeding up the convergence of iteration methods
Boris T Polyak · 1964
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A method of solving a convex programming problem with convergence rate O ( 1 / k 2 ) O(1/k^{2})
Yurii Nesterov · 1983
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Introduction to optimization
Boris T Polyak · 1987
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Geometric numerical integration: structure-preserving algorithms for ordinary differential equations , volume 31
Ernst Hairer, Christian Lubich, and Gerhard Wanner · 2006
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How to make the gradients small
Yurii Nesterov · 2012
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Introductory Lectures on Convex Optimization: A Basic Course , volume 87
Yurii Nesterov · 2013
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A variational perspective on accelerated methods in optimization
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Acceleration and averaging in stochastic descent dynamics
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Michael Betancourt, Michael I Jordan, and Ashia C Wilson · 2018
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Understanding the acceleration phenomenon via high-resolution differential equations
Bin Shi, Simon S Du, Michael I Jordan, and Weijie J Su · 2018
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Direct Runge–Kutta discretization achieves acceleration
Jingzhao Zhang, Aryan Mokhtari, Suvrit Sra, and Ali Jadbabaie · 2018
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Ashia C Wilson, Benjamin Recht, and Michael I Jordan · 2016
Cited alongside, same era.
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