A Differential Equation for Modeling Nesterov's Accelerated Gradient Method: Theory and Insights

Weijie Su; Stephen Boyd; Emmanuel J. Candes

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arXiv · 1503.01243

A Differential Equation for Modeling Nesterov's Accelerated Gradient Method: Theory and Insights

Weijie Su·Stephen Boyd·Emmanuel J. Candes

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Abstract

We derive a second-order ordinary differential equation (ODE) which is the limit of Nesterov's accelerated gradient method. This ODE exhibits approximate equivalence to Nesterov's scheme and thus can serve as a tool for analysis. We show that the continuous time ODE allows for a better understanding of Nesterov's scheme. As a byproduct, we obtain a family of schemes with similar convergence rates. The ODE interpretation also suggests restarting Nesterov's scheme leading to an algorithm, which can be rigorously proven to converge at a linear rate whenever the objective is strongly convex.

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BibTeX RIS

Weijie Su, Stephen Boyd, Emmanuel J. Candes. 2015-03-04. A Differential Equation for Modeling Nesterov's Accelerated Gradient Method: Theory and Insights. https://arxiv.org/abs/1503.01243

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