A systematic approach to Lyapunov analyses of continuous-time models in convex optimization

Understand

First-order methods are often analyzed via their continuous-time models, where their worst-case convergence properties are usually approached via Lyapunov functions.

• In this work, we provide a systematic and principled approach to find and verify Lyapunov functions for classes of ordinary and stochastic differential equations.
• More precisely, we extend the performance estimation framework, originally proposed by Drori and Teboulle [10], to continuous-time models.
• We retrieve convergence results comparable to those of discrete methods using fewer assumptions and convexity inequalities, and provide new results for stochastic accelerated gradient flows.