Computer-Aided Lyapunov Analyses and Counter-Examples to the Convergence of First-Order Optimization Methods

Explore computer-aided Lyapunov analyses and counter-examples to the convergence of first-order optimization methods in this 33-minute conference talk by Adrien Taylor at the Erwin Schrödinger International Institute for Mathematics and Physics. Delve into constructive approaches for discovering Lyapunov functions and their structural properties in the context of first-order optimization algorithms. Learn about methodologies for creating counter-examples when no such Lyapunov functions exist. Examine example-based analyses of simple optimization algorithms like gradient descent, the heavy-ball method, and the Chambolle-Pock algorithm. Gain insights from joint research works on automated convergence guarantees, tight Lyapunov analysis, and provable non-accelerations in optimization methods.