Finding the global minima of objective functions using modified Sturm sequences

The minimisation of the objective function is a common requirement in signal processing. The author addresses the problem of finding all of the global minima of a real-valued objective function f which can be expressed as a polynomial over a finite interval. The approach is based on generating a modified Sturm sequence from f-z where z is the value of f at the global minima. The technique provides the number of the global minima of f, the value of z and the locations of the global minima of f. A simple numerical example is given. While the author concentrates on the one-dimensional case, the extension of the method to multidimensional objective functions is also discussed