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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.
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Received July 13, 2001 / Revised version received March 14, 2002 / Published online October 29, 2002
Mathematics Subject Classification (1991): 65K05, 90C30
Correspondence to: Yaroslav D. Sergeyev
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Kvasov, D., Pizzuti, C. & Sergeyev, Y. Local tuning and partition strategies for diagonal GO methods. Numer. Math. 94, 93–106 (2003). https://doi.org/10.1007/s00211-002-0419-8
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DOI: https://doi.org/10.1007/s00211-002-0419-8