ABSTRACT
In this chapter, the authors examine design methods that involve the application of optimization techniques. These methods are both flexible and versatile and can be used to obtain a variety of filter characteristics. It should be mentioned, however, that the amount of computation required can sometimes be considerable. A class of such algorithms that have been found to be very versatile, efficient, and robust is the class of quasi-Newton algorithms. Quasi-Newton algorithms have a number of important advantages relative to other unconstrained optimization algorithms as follows: the second derivatives of the objective function are not required, matrix inversion is unnecessary, the hereditary property of the Davidon–Fletcher–Powell and Broyden–Fletcher–Goldfarb–Shanno (BFGS) updating formulas eliminates the need to check and possibly manipulate matrix Sk and An inexact line search can be used for the minimization of J (xk + adk.), particularly if the BFGS updating formula is used.
