A deterministic global optimization using smooth diagonal auxiliary functions

• Differentiable black-box global optimization problems are considered.
• A new deterministic ‘Divide-the-Best’ algorithm is proposed in its basic version.
• The method is based on efficient diagonal partitions and smooth auxiliary functions.
• Convergence conditions of the new method are studied.
• Numerical experiments executed on eight hundred test functions are presented.

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)f(x) and its gradient f′(x)f′(x) are black-box functions. It is supposed that f′(x)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.