A global optimization algorithm for multivariate functions with Lipschitzian first derivatives

In this paper we propose a new multi-dimensional method to solve unconstrained global optimization problems with Lipschitzian first derivatives. The method is based on a partition scheme that subdivides the search domain into a set of hypercubes in the course of optimization. This partitioning is regulated by the decision rule that provides evaluation of the ''importance'' of each generated hypercube and selection of some partition element to perform the next iteration. Sufficient conditions of global convergence for the new method are investigated. Results of numerical experiments are also presented.