  In many practical decision-making problems it happens that functions involved
in optimization process are black-box with unknown analytical representations
and hard to evaluate. In this paper, a global optimization problem is
considered where both the goal function~$f(x)$ and its gradient $f'(x)$ are
black-box functions. It is supposed that $f'(x)$ satisfies the Lipschitz
condition over the search hyperinterval with an unknown Lipschitz constant~$K$.
A new deterministic `Divide-the-Best' algorithm based on efficient diagonal
partitions and smooth auxiliary functions is proposed in its basic version, its
convergence conditions are studied and numerical experiments executed on eight
hundred test functions are presented.
