Section: New Results
Lyapunov Functions for First-Order Methods: Tight Automated Convergence Guarantees
In , 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 and integral quadratic constraints, and relies on convex interpolation.