A New Inclusion Function for Optimization: Kite - The One Dimensional Case

In this paper the kite inclusion function is presented for branch-andbound type interval global optimization using at least gradient information. The basic idea comes from the simultaneous usage of the centered forms and the linear boundary value forms. We will show that the new technique is not worse and usually considerably better than these two. The best choice for the center of the kite inclusion will be given. The isotonicity and at least quadratical convergence hold and there is a pruning effect of the kite which is derived from the construction of the inclusion, thus more function evaluations are not needed to use it. A numerical investigation on large standard multiextremal test functions has been done to show the performance.