A new pruning test for finding all global minimizers of nonsmooth functions

A new pruning test is presented via interval slopes for finding all global minimizers of nonsmooth functions of several variables, based on an expansion scheme which can be used to achieve better interval slopes and enclosure of function ranges. The presented pruning test extends Ratz's [A nonsmooth global optimization technique using slopes: one-dimensional case, J. Global Optimiz. 4 (1999) 365-393] pruning technique, which can be extensively applied in several variable nonsmooth global optimization as a accelerating device. This new pruning test is similar to the monotonicity test frequently used in interval methods for smooth problems, but it improves the monotonicity test. Numerical results show that the proposed global optimization algorithm with the new pruning test is better than that with the monotonicity test for smooth functions and superior to other interval algorithm for nonsmooth functions.