Email this article THE METHOD OF FICTITIOUS EXTREMA LOCALIZATION IN THE PROBLEM OF GLOBAL OPTIMIZATION
- Authors: Evtushenko Y.G.1,2, Tret’yakov A.A.1,3
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Affiliations:
- Federal Research Center “Informatics and Control” of the Russian Academy of Sciences
- Moscow Institute of Physics and Technology (National Research University)
- Siedlce University, Faculty of Sciences
- Issue: Vol 512, No 1 (2023)
- Pages: 78-80
- Section: MATHEMATICS
- URL: https://jdigitaldiagnostics.com/2686-9543/article/view/647911
- DOI: https://doi.org/10.31857/S2686954323600222
- EDN: https://elibrary.ru/PNRHVU
- ID: 647911
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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.
About the authors
Yu. G. Evtushenko
Federal Research Center “Informatics and Control” of the Russian Academy of Sciences; Moscow Institute of Physics and Technology (National Research University)
Author for correspondence.
Email: yuri-evtushenko@yandex.ru
Russian Federation, Moscow; Russian Federation, Dolgoprudny, Moscow olast
A. A. Tret’yakov
Federal Research Center “Informatics and Control” of the Russian Academy of Sciences; Siedlce University, Faculty of Sciences
Author for correspondence.
Email: prof.tretyakov@gmail.com
Russian Federation, Moscow; Poland, Siedlce
References
- Евтушенко Ю.Г. Методы решения экстремальных задач и их применение в системах оптимизации. М.: Наука, 1982.
- Карманов В.Г. Математическое программирование. М.: Наука, 1986.
- Grishagin V., Israfilov R., Sergeyev Y. Convergence conditions and numerical comparison of global optimization methods based on dimensionality reduction schemes // Applied Mathematics and Computation. 2018. V. 318. P. 270–280.
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