A deterministic global optimization using smooth diagonal auxiliary functions

In many practical decision-making problems it happens that functions involvedin optimization process are black-box with unknown analytical representationsand hard to evaluate. In this paper, a global optimization problem is considered where both the goal function f(x) and its gradient f'(x) areblack-box functions. It is supposed that f'(x) satisfies the Lipschitz conditionover the search hyperinterval with an unknown Lipschitz constant K. A new deterministic 'Divide-the-Best' algorithm based on efficient diagonalpartitions 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.