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 optimizationmethods. 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. (C) 2010 John Wiley & Sons, Inc.