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We introduce the "continuized" Nesterov acceleration, a close variant of Nesterov acceleration whose variables are indexed by a continuous time parameter.
Accelerated first-order methods: Differential equations and Lyapunov functions
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A method of solving a convex programming problem with convergence rate O ( 1 / k 2 ) O(1/k^{2})
Nesterov, Y. (1983) · 1983
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Introductory Lectures on Convex Optimization: A Basic Course
Nesterov, Y. (2003) · 2003
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Accelerated gradient methods for stochastic optimization and online learning
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Dual averaging methods for regularized stochastic learning and online optimization
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Devolder, O. (2011) · 2011
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Asynchrony and acceleration in gossip algorithms
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An optimal method for stochastic composite optimization
Lan, G. (2012) · 2012
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Limit theorems for stochastic processes
Jacod, J. and Shiryaev, A. (2013) · 2013
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Reversible markov chains and random walks on graphs
Aldous, D. and Fill, J. A. (2002) · 2014
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Stochastic differential equations and diffusion processes
Ikeda, N. and Watanabe, S. (2014) · 2014
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A differential equation for modeling Nesterov’s accelerated gradient method: theory and insights
Su, W., Boyd, S., and Candes, E. (2014) · 2014
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A geometric alternative to Nesterov’s accelerated gradient descent
Bubeck, S., Lee, Y. T., and Singh, M. (2015) · 2015
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From averaging to acceleration, there is only a step-size
Flammarion, N. and Bach, F. (2015) · 2015
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Fast convergence of inertial dynamics and algorithms with asymptotic vanishing viscosity
Attouch, H., Chbani, Z., Peypouquet, J., and Redont, P. (2018) · 2018
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Betancourt, M., Jordan, M., and Wilson, A. (2018) · 2018
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Optimization methods for large-scale machine learning
Bottou, L., Curtis, F. E., and Nocedal, J. (2018) · 2018
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On acceleration with noise-corrupted gradients
Cohen, M., Diakonikolas, J., and Orecchia, L. (2018) · 2018
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Lectures on Convex Optimization
Nesterov, Y. (2018) · 2018
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Understanding the acceleration phenomenon via high-resolution differential equations
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Optimized first-order methods for smooth convex minimization
Kim, D. and Fessler, J. A. (2016) · 2016
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Wibisono, A., Wilson, A. C., and Jordan, M. I. (2016) · 2016
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A Lyapunov analysis of momentum methods in optimization
Wilson, A., Recht, B., and Jordan, M. I. (2016) · 2016
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Direct Runge-Kutta discretization achieves acceleration
Zhang, J., Mokhtari, A., Sra, S., and Jadbabaie, A. (2018) · 2016
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Linear Coupling: An Ultimate Unification of Gradient and Mirror Descent
Allen-Zhu, Z. and Orecchia, L. (2017) · 2017
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Shi, B., Du, S., Jordan, M., and Su, W. (2018) · 2018
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Rate of convergence of the Nesterov accelerated gradient method in the subcritical case α ⩽ 3 \alpha\leqslant 3
Attouch, H., Chbani, Z., and Riahi, H. (2019) · 2019
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The approximate duality gap technique: A unified theory of first-order methods
Diakonikolas, J. and Orecchia, L. (2019) · 2019
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A dynamical systems perspective on Nesterov acceleration
Muehlebach, M. and Jordan, M. (2019) · 2019
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Acceleration via symplectic discretization of high-resolution differential equations
Shi, B., Du, S., Su, W., and Jordan, M. (2019) · 2019
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Robust accelerated gradient methods for smooth strongly convex functions
Aybat, N. S., Fallah, A., Gurbuzbalaban, M., and Ozdaglar, A. (2020) · 2020
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Acceleration methods
d’Aspremont, A., Scieur, D., and Taylor, A. (2021) · 2021
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