Global search acceleration in the nested optimization scheme

Multidimensional unconstrained global optimization problem with objective function under Lipschitz condition is considered. For solving this problem the dimensionality reduction approach on the base of the nested optimization scheme is used. This scheme reduces initial multidimensional problem to a family of one-dimensional subproblems being Lipschitzian as well and thus allows applying univariate methods for the execution of multidimensional optimization. For two well-known one-dimensional methods of Lipschitz optimization the modifications providing the acceleration of the search process in the situation when the objective function is continuously differentiable in a vicinity of the global minimum are considered and compared. Results of computational experiments on conventional test class of multiextremal functions confirm efficiency of the modified methods.