Global Optimization

Abstract

We want to find the global minimum in an interval [x] of a function f that may have many local minima. We want to compute the minimum value of f and the point(s) at which the minimum value is attained. This is a very difficult problem for classical methods because narrow, deep valleys may escape detection. In contrast, the interval method presented here evaluates f on a continuum of points, including those points that are not finitely represent able, so valleys, no matter how narrow, are recognized with certainty. Further, interval techniques often can reject large regions in which the optimum can be guaranteed not to lie, so they can be faster overall than classical methods for many problems.