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Method for False Extrema Localization in Global Optimization

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Abstract

The problem of finding the global minimum of a nonnegative function on a positive parallelepiped in n-dimensional Euclidean space is considered. A method for localizing false extrema in a bounded domain near the origin is proposed, which allows one to separate the global minimum from the false ones by moving the former away from the latter. With a suitable choice of the starting point in the gradient descent method, it is possible to prove the convergence of the iterative sequence to the global minimum of the function.

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REFERENCES

  1. Yu. G. Evtushenko, Methods for Solving Optimization Problems and Their Applications in Optimization Systems (Nauka, Moscow, 1982) [in Russian].

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  2. V. G. Karmanov, Mathematical Programming (Nauka, Moscow, 2000) [in Russian].

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  3. V. Grishagin, R. Israfilov, and Y. Sergeyev, “Convergence conditions and numerical comparison of global optimization methods based on dimensionality reduction schemes,” Appl. Math. Comput. 318, 270–280 (2018).

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Funding

This work was supported by the Russian Science Foundation, project no. 21-71-30005.

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Authors and Affiliations

  1. Federal Research Center “Informatics and Control,” Russian Academy of Sciences, Moscow, Russia

    Yu. G. Evtushenko & A. A. Tret’yakov

  2. Moscow Institute of Physics and Technology (National Research University), Dolgoprudnyi, Moscow oblast, Russia

    Yu. G. Evtushenko

  3. Faculty of Exact and Natural Sciences, Siedlce University, Siedlce, Poland

    A. A. Tret’yakov

Authors
  1. Yu. G. Evtushenko
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  2. A. A. Tret’yakov
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Corresponding authors

Correspondence to Yu. G. Evtushenko or A. A. Tret’yakov.

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The authors declare that they have no conflicts of interest.

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Translated by I. Ruzanova

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Evtushenko, Y.G., Tret’yakov, A.A. Method for False Extrema Localization in Global Optimization. Dokl. Math. 108, 309–311 (2023). https://doi.org/10.1134/S1064562423700850

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  • DOI: https://doi.org/10.1134/S1064562423700850

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