Multidimensional global optimization algorithm based on adaptive diagonal curves

A classical global optimization problem is considered: minimization of a multidimensional multiextremal function that is Lipschitzian on a hyperinterval. A new information statistical algorithm for solving this problem is suggested. The new method relies on adaptive diagonal curves that combine the ideas of diagonal algorithms and Peano curves. Conditions for global convergence of the suggested algorithm are established. The results of extensive numerical experiments are presented to demonstrate the advantage of the new method as compared to conventional diagonal global optimization algorithms. The experiments corroborate the theoretical conclusion that the advantage of the new method increases with the problem dimension.