A Derivation of Nesterov’s Accelerated Gradient Algorithm from 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

Enhancements to the DIDO© Optimal Control Toolbox

In 2020, DIDO© turned 20! The software package emerged in 2001 as a basic, user-friendly MATLAB teaching tool to illustrate the various nuances of Pontryagin’s Principle but quickly rose to prominence in 2007 after NASA announced it had executed a globally optimal maneuver using DIDO. Since then, the toolbox has grown in applications well beyond … Read more

An optimal control theory for accelerated optimization

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 Citation unpublished Article Download View An optimal control theory for accelerated optimization

Path Constraints in Tychastic and Unscented Optimal Control: Theory, Applications and Experimental Results

In recent papers, we have shown that a Lebesgue-Stieltjes optimal control theory forms the foundations for unscented optimal control. In this paper, we further our results by incorporating uncertain mixed state-control constraints in the problem formulation. We show that the integrated Hamiltonian minimization condition resembles a semi-infinite type mathematical programming problem. The resulting computational difficulties … Read more