Nesterov's Method for Convex Optimization

While Nesterov's algorithm for computing the minimum of a convex function is now over forty years old, it is rarely presented in texts for a first course in optimization. This is unfortunate since for many problems this algorithm is superior to the ubiquitous steepest descent algorithm, and it is equally simple to implement. This article presents an elementary analysis of Nesterov's algorithm that parallels that of steepest descent. It is envisioned that this presentation of Nesterov's algorithm could easily be covered in a few lectures following the introductory material on convex functions and steepest descent included in every course on optimization.