lie derivative – Optimization Online

A Derivation of Nesterov’s Accelerated Gradient Algorithm from Optimal Control Theory

Published: 2021/08/28

Convex Optimization accelerated optimization, control lyapunov function, lie derivative, singular optimal control theory

Nesterov’s accelerated gradient algorithm is derived from first principles. The first principles are founded on the recently-developed optimal control theory for optimization. The necessary conditions for optimal control generate a controllable dynamical system for accelerated optimization. Stabilizing this system via a control Lyapunov function generates an ordinary differential equation. An Euler discretization of the differential … Read more

An optimal control theory for accelerated optimization

Published: 2019/02/24, Updated: 2019/05/19

Isaac Ross

Convex and Nonsmooth Optimization, Unconstrained Optimization accelerated newton's method, control lyapunov function, lie derivative, nesterov's accelerated gradient method, polyak's heavy ball method, riemannian metric, transversality mapping principle

Accelerated optimization algorithms can be generated using a double-integrator model for the search dynamics imbedded in an optimal control problem. Citation unpublished Article Download View An optimal control theory for accelerated optimization