Applications of interval arithmetic in non-smooth global optimization

Abstract

In this paper, an expansion scheme for general functions is presented, which can be used to achieve better enclosure of function ranges. In the context of interval branch-and-bound methods for non-smooth global optimization, a pruning technique is given via the expansion. An interval pruning test is established. This pruning test offers the possibility to cut away a large part of the currently investigated box by the optimization algorithm, which can be utilized as an accelerating device similar to the monotonicity test frequently used in interval methods for smooth problems. Numerical computation shows that the proposed method is reliable and can find all solutions of global optimization problem.