The Connections Between Lyapunov Functions for Some Optimization Algorithms and Differential Equations

In this manuscript we study the properties of a family of a second-order differential equations with damping, its discretizations, and their connections with accelerated optimization algorithms for mstrongly convex and Lsmooth functions. In particular, using the linear matrix inequality (LMI) framework developed by Fazlyab et. al. (2018), we derive analytically a (discrete) Lyapunov function for a two-parameter family of Nesterov...