  In this paper, global optimization (GO) Lipschitz problems are considered
where the multi-dimensional multiextremal objective function is determined over
a hyperinterval. An efficient one-dimensional GO method using local tuning on
the behavior of the objective function is generalized to the multi-dimensional
case by the diagonal approach using two partition strategies. Global
convergence conditions are established for the obtained diagonal geometric
methods. Results of a wide numerical comparison show a strong acceleration
reached by the new methods working with estimates of the local Lipschitz
constants over different subregions of the search domain in comparison with the
traditional approach.
