Numerical methods for continuous global optimization are investigated in this contribution. They are based on the dimensionality reduction approach consisting in the extension of one-dimensional methods to the multidimensional case, as, for example, in the nested optimization scheme. An analytical representation of the objective function is supposed to be unknown (the so-called black-box statement) and, therefore, each evaluation of the objective function at a feasible point is computationally demanding. To model such problems, the Lipschitz condition can be successfully used estimating the unknown Lipschitz constant during the search for the global minimum. Local information about the behavior of the objective function (such as improved estimates of local Lipschitz constants) is taken into account in this work to accelerate the global search. Numerical results illustrate the benefits from the use of local information in global optimization methods constructed in the framework of the dimensionality reduction schemes.