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Zhurnal Srednevolzhskogo Matematicheskogo Obshchestva, 2022, Volume 24, Number 4, Pages 399–418
DOI: https://doi.org/10.15507/2079-6900.24.202204.399-418
(Mi svmo841)
 

This article is cited in 1 scientific paper (total in 1 paper)

Mathematics

Continuous global optimization of multivariable functions based on Sergeev and Kvasov diagonal approach

V. I. Zabotin, P. A. Chernyshevsky

Kazan National Research Technical University named after A. N. Tupolev
Full-text PDF (795 kB) Citations (1)
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Abstract: One of modern global optimization algorithms is method of Strongin and Piyavskii modified by Sergeev and Kvasov diagonal approach. In recent paper we propose an extension of this approach to continuous multivariable functions defined on the multidimensional parallelepiped. It is known that Sergeev and Kvasov method applies only to a Lipschitz continuous function though it effectively extends one-dimensional algorithm to multidimensional case. So authors modify We modify mentioned method to a continuous functions using introduced by Vanderbei $\varepsilon$-Lipschitz property that generalizes conventional Lipschitz inequality. Vanderbei proved that a real valued function is uniformly continuous on a convex domain if and only if it is $\varepsilon$-Lipschitz. Because multidimensional parallelepiped is a convex compact set, we demand objective function to be only continuous on a search domain. We describe extended Strongin’s and Piyavskii’s methods in the Sergeev and Kvasov modification and prove the sufficient conditions for the convergence. As an example of proposed method’s application, at the end of this article we show numerical optimization results of different continuous but not Lipschitz functions using three known partition strategies: “partition on 2”, “partition on 2N” and “effective”. For the first two of them we present formulas for computing a new iteration point and for recalculating the $\varepsilon$-Lipschitz constant estimate. We also show algorithm modification that allows to find a new search point on any algorithm's step.
Keywords: global optimization, non-Lipschitz optimization, nonconvex optimization, $\varepsilon $-Lipschitz function, continuous function, convergence.
Document Type: Article
UDC: 519.853.6
MSC: 90C26
Language: Russian
Citation: V. I. Zabotin, P. A. Chernyshevsky, “Continuous global optimization of multivariable functions based on Sergeev and Kvasov diagonal approach”, Zhurnal SVMO, 24:4 (2022), 399–418
Citation in format AMSBIB
\Bibitem{ZabChe22}
\by V.~I.~Zabotin, P.~A.~Chernyshevsky
\paper Continuous global optimization of multivariable functions based on Sergeev and Kvasov diagonal approach
\jour Zhurnal SVMO
\yr 2022
\vol 24
\issue 4
\pages 399--418
\mathnet{http://mi.mathnet.ru/svmo841}
\crossref{https://doi.org/10.15507/2079-6900.24.202204.399-418}
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  • This publication is cited in the following 1 articles:
    Citing articles in Google Scholar: Russian citations, English citations
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    Zhurnal Srednevolzhskogo Matematicheskogo Obshchestva
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