Remarks on global optimization using space-filling curves

The problem of finding the global minimum of a real function on a set S ⊆ R^N occurs in many real world problems. In this paper, the global optimization problem with a multiextremal objective function satisfying the Lipschitz condition over a hypercube is considered. We propose a local tuning technique that adaptively estimates the local Lipschitz constants over different zones of the search region and a technique, called the local improvement, in order to accelerate the search. Peano-type space-filling curves for reduction of the dimension of the problem are used. Convergence condition are given. Numerical experiments executed on several hundreds of test functions show quite a promising performance of the introduced acceleration techniques.