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We show that accelerated optimization methods can be seen as particular instances of multi-step integration schemes from numerical analysis, applied to the gradient flow equation.
Some methods of speeding up the convergence of iteration methods
Boris T Polyak · 1964
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Monotone operators and the proximal point algorithm
R Tyrrell Rockafellar · 1976
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G-stability is equivalent toa-stability
Germund Dahlquist · 1978
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On one-leg multistep methods
Germund Dahlquist · 1983
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A method of solving a convex programming problem with convergence rate o (1/k2)
Yurii Nesterov · 1983
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Implicit-explicit methods for time-dependent partial differential equations
Uri M Ascher, Steven J Ruuth, and Brian TR Wetton · 1995
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On the stability of implicit-explicit linear multistep methods
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Lectures on modern convex optimization: analysis, algorithms, and engineering applications
Aharon Ben-Tal and Arkadi Nemirovski · 2001
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Mirror descent and nonlinear projected subgradient methods for convex optimization
Amir Beck and Marc Teboulle · 2003
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An introduction to numerical analysis
Endre Süli and David F Mayers · 2003
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Thirty years of g-stability
JC Butcher · 2006
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The Łojasiewicz inequality for nonsmooth subanalytic functions with applications to subgradient dynamical systems
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Gradient methods for minimizing composite objective function, 2007
Yurii Nesterov et al · 2007
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John C Duchi, Shai Shalev-Shwartz, Yoram Singer, and Ambuj Tewari · 2010
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Numerical analysis
Walter Gautschi · 2011
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A geometric alternative to nesterov’s accelerated gradient descent
S. Bubeck, Y. Tat Lee, and M. Singh · 2015
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Accelerated mirror descent in continuous and discrete time
Walid Krichene, Alexandre Bayen, and Peter L Bartlett · 2015
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Universal gradient methods for convex optimization problems
Yurii Nesterov · 2015
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Analysis and design of optimization algorithms via integral quadratic constraints
Laurent Lessard, Benjamin Recht, and Andrew Packard · 2016
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A variational perspective on accelerated methods in optimization
Andre Wibisono, Ashia C Wilson, and Michael I Jordan · 2016
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Introductory lectures on convex optimization: A basic course , volume 87
Yurii Nesterov · 2013
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A differential equation for modeling nesterov’s accelerated gradient method: Theory and insights
Weijie Su, Stephen Boyd, and Emmanuel Candes · 2014
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Ashia C Wilson, Benjamin Recht, and Michael I Jordan · 2016
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Stability and convergence analysis of implicit–explicit one-leg methods for stiff delay differential equations
Gengen Zhang and Aiguo Xiao · 2016
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Linear coupling: An ultimate unification of gradient and mirror descent
Zeyuan Allen Zhu and Lorenzo Orecchia · 2017
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