Diagonal numerical methods for solving Lipschitz global optimization problems

This paper briefly describes some results of the author's PhD thesis, which has been specially mentioned by the Italian INdAM-SIMAI Committee for the Competition "The Best PhD Thesis in Applied Mathematics defended in 2004-2006". In this work, 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.