This article is cited in 17 papers

Homogeneous algorithms for multiextremal optimization

S. M. Elsakov, V. I. Shiryaev

Southern Ural State University, pr. Lenina 76, Chelyabinsk, 454080 Russia

Abstract: The class of homogeneous algorithms for multiextremal optimization is defined, and a number of theorems are proved, including a sufficient condition for the convergence of homogeneous algorithms to a global minimizer. An approach to the synthesis of homogeneous algorithms based on model multi-peak functions is proposed. The existing algorithms are reviewed, and a new efficient multidimensional algorithm based on the Delaunay triangulation is constructed. Some numerical results are presented.

Key words: global optimization, homogeneous algorithms, Delaunay triangulation, convergence of homogeneous algorithm to a global minimizer.

UDC: 519.626

Received: 22.11.2006
Revised: 05.12.2008

 English version: Computational Mathematics and Mathematical Physics, 2010, 50:10, 1642–1654

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