Method for False Extrema Localization in Global Optimization

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...

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Veröffentlicht in:Doklady. Mathematics 2023-08, Vol.108 (1), p.309-311
Hauptverfasser: Evtushenko, Yu. G., Tret’yakov, A. A.
Format: Artikel
Sprache:eng
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Zusammenfassung: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.
ISSN:1064-5624
1531-8362
DOI:10.1134/S1064562423700850