Steepest descent

The steepest descent method has a rich history and is one of the simplest and best known methods for minimizing a function. While the method is not commonly used in practice due to its slow convergence rate, understanding the convergence properties of this method can lead to a better understanding of many of the more sophisticated optimization methods. Here, we give a short introduction and discuss some of the advantages and disadvantages of this method. Some recent results on modified versions of the steepest descent method are also discussed.