Multidimensional global optimization using numerical estimates of objective function derivatives

Abstract

This paper proposes a method for solving the computation-costly multidimensional global optimization problems. The method is efficient in the one-dimensional case and its combination with the nested reduction scheme competitive with optimization methods reducing multidimensional problems by using space-filling (Peano) curves. The developed method is based on an approach, in which not only the minimized function values but also the values of derivatives of these functions are used to increase the efficiency of global optimization. The required values of the derivatives are estimated numerically by handling the available search information. The results of the executed experiments confirm the developed approach is promising.