Improved Lipschitz bounds with the first norm for function values over multidimensional simplex. (English) Zbl 1182.90073

Paulavičius, R.; Žilinskas, J.

Math. Model. Anal. 13, No. 4, 553-563 (2008).

Summary: A branch and bound algorithm for global optimization is proposed, where the maximum of an upper bounding function based on Lipschitz condition and the first norm over a simplex is used as the upper bound of function. In this case the graph of bounding function is intersection of n-dimensional pyramids and its maximum point is found solving a system of linear equations. The efficiency of the proposed global optimization algorithm is evaluated experimentally.

MSC:

90C26	Nonconvex programming, global optimization
90C57	Polyhedral combinatorics, branch-and-bound, branch-and-cut

Keywords:

first norm