Global Optimization of a Perturbed Problem Using Interval Analysis

Abstract

When parameters are measured quantities and these measurements are subject to error, perturbed problems may arise. We suppose that intervals containing the values of these parameters are known. When parameter value changes, the location of the global minimum can change discontinuously. We propose an interval method to determine the optimal solution of a given problem under such conditions. When the box size torelance is small, large perturbations require many boxes to cover the solution set. We describe a method that bounds the solution set without covering it by a large number of small boxes.