Generation of <i>α</i>‐dense curves in a cube of IRⁿ

Abstract

A multi‐dimensional global optimization method has been developed. This method uses the curves of IR n called α ‐dense. A characterization of α ‐dense curves is given in terms of γ ‐stochastically independent functions as well as a constructive method to generate them by means of only one function φ called γ ‐uniformly distributed has been developed. A very large class of functions which generate α ‐dense curves is discussed. This class contains the γ ‐uniformly distributed functions, the periodic functions and even functions which are not periodic, but which fulfil some properties.