Global minimization using space-filling curves

In this paper the global optimization problem of a multiextremal function satisfying the Lipschitz condition over a hyperinterval is considered. To solve it we propose algorithms that use Peano-type space-flling curves for reduction of dimensionality. The knowledge of the Lipschitz constant is not required. Local tuning on the behavior of the objective function and a new technique, named local improvement, are used in order to accelerate the search. Convergence condition are given. Numerical experiments show quite promising performance of the new technique.