×

Search for a global extremum in a certain subclass of functions with the Lipschitz condition. (English. Russian original) Zbl 0608.90088

Cybernetics 21, 812-819 (1985); translation from Kibernetika 1985, No. 6, 72-76 (1985).
The realization of a sequential algorithm to find the global extremum of functions satisfying the Lipschitz condition is described. It is shown that in a certain subclass of the Lipschitz class this algorithm possesses a logarithmic dependence of the quantity of operations on the error.

MSC:

90C30 Nonlinear programming
65K05 Numerical mathematical programming methods
49M37 Numerical methods based on nonlinear programming
PDFBibTeX XMLCite
Full Text: DOI

References:

[1] Yu. M. Danilin and S. A. Piyavskii, ?On an algorithm seeking the absolute minium,? Teoriya Optim. Reshenii, No. 2, 25?37 (1967).
[2] L. N. Timonov, ?Algorithm to search for the global extremum,? Izv. Akad. Nauk SSSR, Tekh. Kibern., No. 3, 53?60 (1977).
[3] Yu. M. Danilin, ?Estimate of the efficiency of an algorithm to seek the absolute minimum,? Zh. Vychisl. Mat. Mat. Fiz.,11, No. 4, 1026?1031 (1971).
[4] V. V. Ivanov, ?On optimal algorithms for minimization of functions of certain classes,? Kibernetika, No. 4, 81?94 (1972).
[5] D. Knute, Art of Programming on Electronic Computers [Russian translation], Vol. 3, Mir, Moscow (1978).
This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. In some cases that data have been complemented/enhanced by data from zbMATH Open. This attempts to reflect the references listed in the original paper as accurately as possible without claiming completeness or a perfect matching.