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Zh. Vychisl. Mat. Mat. Fiz., 2010, Volume 50, Number 10, Pages 1727–1740 (Mi zvmmf4944)  

This article is cited in 9 scientific papers (total in 9 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.

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

Bibliographic databases:

UDC: 519.626
Received: 22.11.2006
Revised: 05.12.2008

Citation: S. M. Elsakov, V. I. Shiryaev, “Homogeneous algorithms for multiextremal optimization”, Zh. Vychisl. Mat. Mat. Fiz., 50:10 (2010), 1727–1740; Comput. Math. Math. Phys., 50:10 (2010), 1642–1654

Citation in format AMSBIB
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    Citing articles on Google Scholar: Russian citations, English citations
    Related articles on Google Scholar: Russian articles, English articles

    This publication is cited in the following articles:
    1. Elsakov S.M., “Primenenie odnorodnogo algoritma globalnoi optimizatsii dlya resheniya prakticheskikh zadach”, Aktualnye problemy gumanitarnykh i estestvennykh nauk, 2010, no. 12, 48–61  elib
    2. Elsakov S.M., Shiryaev V.I., “Odnorodnye algoritmy mnogoekstremalnoi optimizatsii dlya tselevykh funktsii so znachitelnym vremenem vychisleniya znacheniya”, Vychislitelnye metody i programmirovanie: novye vychislitelnye tekhnologii, 12:1 (2011), 48–69  mathnet  elib
    3. Žilinskas A., “On strong homogeneity of two global optimization algorithms based on statistical models of multimodal objective functions”, Appl. Math. Comput., 218:16 (2012), 8131–8136  crossref  mathscinet  zmath  isi  elib  scopus
    4. Paulavicius R., Sergeyev Ya.D., Kvasov D.E., Zilinskas J., “Globally-Biased Disimpl Algorithm For Expensive Global Optimization”, J. Glob. Optim., 59:2-3, SI (2014), 545–567  crossref  mathscinet  zmath  isi  elib  scopus
    5. Shiryaev V., Tsybulevsky A., “Homogeneous Algorithm For Global Optimization With Adaptive Model of Objective Function”, 2016 2Nd International Conference on Industrial Engineering, Applications and Manufacturing (Icieam), IEEE, 2016  isi
    6. Liu Q., Yang G., Zhang Zh., Zeng J., “Improving the convergence rate of the DIRECT global optimization algorithm”, J. Glob. Optim., 67:4 (2017), 851–872  crossref  mathscinet  zmath  isi  scopus
    7. Pardalos P., Zilinskas A., Zilinskas J., “Non-Convex Multi-Objective Optimization”, Non-Convex Multi-Objective Optimization, Springer Optimization and Its Applications, 123, Springer International Publishing Ag, 2017, 1–192  crossref  mathscinet  isi
    8. Sergeyev Ya.D., Kvasov D.E., Mukhametzhanov M.S., “On Strong Homogeneity of a Class of Global Optimization Algorithms Working With Infinite and Infinitesimal Scales”, Commun. Nonlinear Sci. Numer. Simul., 59 (2018), 319–330  crossref  mathscinet  isi  scopus
    9. Kvasov D.E. Mukhametzhanov M.S. Sergeyev Ya.D., “III-Conditioning Provoked By Scaling in Univariate Global Optimization and Its Handling on the Infinity Computer”, AIP Conference Proceedings, 2070, ed. Emmerich M. Deutz A. Hille S. Sergeyev Y., Amer Inst Physics, 2019, 020011  crossref  isi
  • Журнал вычислительной математики и математической физики Computational Mathematics and Mathematical Physics
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