AN ALGORITHM FOR SOLVING SOME NONLINEAR SYSTEMS WITH APPLICATIONS TO EXTREMUM PROBLEMS

We consider a class of nonlinear systems for which a positive solution exists and is unique. Such systems appear quite naturally in several applications concerning difference equations. Moreover, certain extremum problems can be reduced to solving these systems. In order to solve such problems we develop a quasi-Newton algorithm which is very efficient just because the existence and uniqueness of the solution are guaranteed. Several numerical examples illustrate the general results.