Optimal Multisections in Interval Branch-and-Bound Methods of Global Optimization

In this paper we define multisections of intervals that yield sharp lower bounds in branch-and-bound type methods for interval global optimization. A so called 'generalized kite', defined for differentiable univariate functions, is built simultaneously with linear boundary forms and suitably chosen centered forms. Proofs for existence and uniqueness of optimal cuts are given. The method described may be used either as an accelerating device or in a global optimization algorithm with an efficient pruning effect. A more general principle for decomposition of boxes is suggested.