From the summary: A global optimization problem is considered where the objective function is a multidimensional black-box function satisfying the Lipschitz condition over a hyperinterval and hard to evaluate. Such functions are frequently encountered in practice that explains a great interest of researchers to the stated problem. A new diagonal scheme which is aimed for developing fast global optimization algorithms is presented, and several such algorithms are introduced and examined. Theoretical and experimental studies performed confirm the benefit of the new approach over traditionally used diagonal global optimization methods.