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In this paper, global optimization (GO) Lipschitz problems are consideredwhere the multi-dimensional multiextremal objective function is determined overa hyperinterval. An efficient one-dimensional GO method using local tuning onthe behavior of the objective function is generalized to the multi-dimensionalcase by the diagonal approach using two partition strategies. Globalconvergence conditions are established for the obtained diagonal geometricmethods. Results of a wide numerical comparison show a strong accelerationreached by the new methods working with estimates of the local Lipschitzconstants over different subregions of the search domain in comparison with thetraditional approach.

Local tuning and partition strategies for diagonal GO methods