A BRANCH-AND-PRUNE METHOD FOR GLOBAL OPTIMIZATION The Univariate Case
Dimitris G. Sotiropoulos, T. N. Grapsa · 2001
We present a branch-and-prune algorithm for univariate optimization. Pruning is achieved by using first order information of the objective function by means of an interval evaluation of the derivative over the current interval. First order information aids fourfold. Firstly, to check monotonicity. Secondly, to determine optimal centers which, along with the mean value form, are used to improve the enclosure of the function range. Thirdly, to prune the search interval using the current upper bound of the global minimum, and finally, to apply a more sophisticated splitting strategy. Results of numerical experiments are also presented. 1.