The Determination of the Location of the Global Maximum of a Function in the Presence of Several Local Extrema

The global maximum of a function can be determined by using information about the number of stationary points in the domain of interest. This information is obtained by evaluating an integral that equals the exact number of stationary points of the function. The integral is based on work by Kronecker and Picard at the end of the nineteenth century. The numerical feasibility of the method is shown by two computed examples, i.e., estimation problems from statistics and optical communication theory. In these examples the global maximum of the likelihood function is obtained by using the total number of stationary points as revealed by the computed integral.