Lipschitz global optimization with derivatives

In this work, a global optimization problem is considered where both the objective function f(x) and its gradient f'(x) are black-box multiextremal functions. It is supposed that f'(x) satisfies the Lipschitz condition over the search hyperintervalwith an unknown Lipschitz constant K. A number of geometric Lipschitz global optimization methods based on constructing auxiliary functions with the usage of different estimates of the Lipschitz constant K are presented in this communication. Results of their systematic experimental investigation are also given.