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Doklady Rossijskoj Akademii Nauk. Mathematika, Informatika, Processy Upravlenia, 2023, Volume 512, Pages 78–80
DOI: https://doi.org/10.31857/S2686954323600222 (Mi danma402) 		 
MATHEMATICS

The method of fictitious extrema localization in the problem of global optimization

Yu. G. Evtushenkoab, A. A. Tret'yakovac

a Federal Research Center "Computer Science and Control" of Russian Academy of Sciences, Moscow
b Moscow Institute of Physics and Technology (National Research University), Dolgoprudny, Moscow Region
c Siedlce University, Faculty of Sciences, Siedlce, Poland
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DOI: https://doi.org/10.31857/S2686954323600222
Abstract: The problem of finding the global extremum of a non-negative function on a positive parallelepiped in $n$-dimensional Euclidean space is considered. A method of fictitious extrema localization in a bounded area near the origin is proposed, which allows to separate the global extremum point from fictitious extrema by discarding it at a significant distance from the localization set of fictitious minima. At the same time, due to the choice of the starting point in the gradient descent method, it is possible to justify the convergence of the iterative sequence to the global extremum of the minimized function.
Keywords: global extremum, local minimum, gradient descent method, convergence.
Funding agency Grant number
Russian Science Foundation 21-71-30005
This work was supported by the Russian Science Foundation, project no. 21-71-30005.
Received: 19.04.2023
Revised: 04.07.2023
Accepted: 13.07.2023
English version:
Doklady Mathematics, 2023, Volume 108, Issue 1, Pages 309–311
DOI: https://doi.org/10.1134/S1064562423700850
Bibliographic databases:
Document Type: Article
UDC: 519.615
Language: Russian
Citation: Yu. G. Evtushenko, A. A. Tret'yakov, “The method of fictitious extrema localization in the problem of global optimization”, Dokl. RAN. Math. Inf. Proc. Upr., 512 (2023), 78–80; Dokl. Math., 108:1 (2023), 309–311
Citation in format AMSBIB
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\by Yu.~G.~Evtushenko, A.~A.~Tret'yakov
\paper The method of fictitious extrema localization in the problem of global optimization
\jour Dokl. RAN. Math. Inf. Proc. Upr.
\yr 2023
\vol 512
\pages 78--80
\mathnet{http://mi.mathnet.ru/danma402}
\crossref{https://doi.org/10.31857/S2686954323600222}
\elib{https://elibrary.ru/item.asp?id=54538910}
\transl
\jour Dokl. Math.
\yr 2023
\vol 108
\issue 1
\pages 309--311
\crossref{https://doi.org/10.1134/S1064562423700850}
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