The problem of finding the global minimum of a real function on a set S ⊆ RN 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.
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Research Article| October 20 2016
Remarks on global optimization using space-filling curves
AIP Conf. Proc. 1776, 060010 (2016)
Daniela Lera, Yaroslav Sergeyev; Remarks on global optimization using space-filling curves. AIP Conf. Proc. 20 October 2016; 1776 (1): 060010. https://doi.org/10.1063/1.4965344
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