Interval Newton methods and perturbed problems

Abstract

This paper describes a straightforward implementation of a modified Newton algorithm which generates the best interval bounding the solution generated using interval Newton methods. This implementation addresses the issues described by Hansen and Greenberg for analyzing problems with data perturbations using interval analysis. It also indicates a new approach of potentially attractive methods for using interval Newton methods. While our focus is on perturbed problems (sensitivity analysis), the results are more generally applicable. The major difference in the point of view of perturbed problems versus the general use of interval methods is that in perturbed problems we are focused on the behavior of the function around an optimal solution. The more general approach seeks to identify all optimal solutions of the function.