Locating, characterizing and computing the stationary points of a function

Abstract

A method for the localization, characterization and computation of the stationary points of a continuously differentiable real-valued function ofn variables is presented. It is based on the combinatorial topology concept of the degree of a mapping associated with an oriented polyhedron. The method consists of two principal steps: (i) localization (and computation if required) of a stationary point in ann-dimensional polyhedron; (ii) characterization of a stationary point as a minimum, maximum or saddle point. The method requires only the signs of gradient values to be correct and it can be successfully applied to problems with imprecise values.