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arXiv · 1803.06073

Lyapunov Functions for First-Order Methods: Tight Automated Convergence Guarantees

Adrien Taylor·Bryan Van Scoy·Laurent Lessard
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Abstract

We present a novel way of generating Lyapunov functions for proving linear convergence rates of first-order optimization methods. Our approach provably obtains the fastest linear convergence rate that can be verified by a quadratic Lyapunov function (with given states), and only relies on solving a small-sized semidefinite program. Our approach combines the advantages of performance estimation problems (PEP, due to Drori & Teboulle (2014)) and integral quadratic constraints (IQC, due to Lessard et al. (2016)), and relies on convex interpolation (due to Taylor et al. (2017c;b)).

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BibTeXRIS

Adrien Taylor, Bryan Van Scoy, Laurent Lessard. 2018-03-16. Lyapunov Functions for First-Order Methods: Tight Automated Convergence Guarantees. https://arxiv.org/abs/1803.06073

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