Global optimization using space filling curves

Abstract

The existence of space filling curves opens the way to reducing multivariate optimization problems to the minimization of univariate functions. In this paper, we analyze the Hoelder continuity of space filling curves and exploit this property in the solution of global optimization problems. Subsequently, an algorithm for minimizing univariate Hoelder continuous functions is presented and analyzed. It is shown that the algorithm computes the approximate minimum with the guaranteed precision. The algorithm is tested on some types of two-dimensional functions.