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RAS PresidiumДоклады Российской академии наук. Математика, информатика, процессы управления Doklady Mathematics

  • ISSN (Print) 2686-9543
  • ISSN (Online) 3034-5049

THE METHOD OF FICTITIOUS EXTREMA LOCALIZATION IN THE PROBLEM OF GLOBAL OPTIMIZATION

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PII
10.31857/S2686954323600222-1
DOI
10.31857/S2686954323600222
Publication type
Status
Published
Authors
Yu. G. Evtushenko
  • Affiliation:
    Federal Research Center “Informatics and Control” of the Russian Academy of Sciences
    Moscow Institute of Physics and Technology (National Research University)
A. A. Tret’yakov
  • Affiliation:
    Federal Research Center “Informatics and Control” of the Russian Academy of Sciences
    Siedlce University, Faculty of Sciences
Volume/ Edition
Volume 512 / Issue number 1
Pages
78-80
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
глобальный экстремум локальный минимум градиентный метод сходимость
Date of publication
01.05.2023
Year of publication
2023
Number of purchasers
0
Views
35

References

  1. 1. Евтушенко Ю.Г. Методы решения экстремальных задач и их применение в системах оптимизации. М.: Наука, 1982.
  2. 2. Карманов В.Г. Математическое программирование. М.: Наука, 1986.
  3. 3. 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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