Improved lipschitz bounds with the first norm for function values over multidimensional simplex

Abstract

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.