A nonsmooth global optimization technique using slopes: The one-dimensional case (Q1304345)

The author describes a method for computing verified enclosures for the global minimum and all global minimum points of a nonsmooth one-dimensional function subject to bound constraints. The method incorporates a special pruning step generated by interval slopes. This pruning step can be utilized as an accelerating device similar to the monotonicity test frequently used in interval methods for smooth problems. It offers the possibility to cut away a large part of the current box irrespective of the fact that the slope interval contains zero or not.