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An algorithm of simplicial Lipschitz optimization with the bi-criteria selection of simplices for the bi-section

Author

Listed:
  • Albertas Gimbutas

    (Vilnius University)

  • Antanas Žilinskas

    (Vilnius University)

Abstract

An algorithm of simplicial optimization is proposed where a bi-criteria selection of a simplex for the bi-section is applied. The first criterion is the minimum of estimated Lipschitz lower bound over the considered simplex. The second criterion is the diameter of the simplex. The results of experimental testing are included.

Suggested Citation

  • Albertas Gimbutas & Antanas Žilinskas, 2018. "An algorithm of simplicial Lipschitz optimization with the bi-criteria selection of simplices for the bi-section," Journal of Global Optimization, Springer, vol. 71(1), pages 115-127, May.
    • Handle: RePEc:spr:jglopt:v:71:y:2018:i:1:d:10.1007_s10898-017-0550-9
    DOI: 10.1007/s10898-017-0550-9
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    References listed on IDEAS

    as
    1. Qunfeng Liu & Jinping Zeng & Gang Yang, 2015. "MrDIRECT: a multilevel robust DIRECT algorithm for global optimization problems," Journal of Global Optimization, Springer, vol. 62(2), pages 205-227, June.
    2. Remigijus Paulavičius & Yaroslav Sergeyev & Dmitri Kvasov & Julius Žilinskas, 2014. "Globally-biased Disimpl algorithm for expensive global optimization," Journal of Global Optimization, Springer, vol. 59(2), pages 545-567, July.
    3. Antanas Žilinskas, 2010. "On similarities between two models of global optimization: statistical models and radial basis functions," Journal of Global Optimization, Springer, vol. 48(1), pages 173-182, September.
    4. Yaroslav D. Sergeyev & Marat S. Mukhametzhanov & Dmitri E. Kvasov & Daniela Lera, 2016. "Derivative-Free Local Tuning and Local Improvement Techniques Embedded in the Univariate Global Optimization," Journal of Optimization Theory and Applications, Springer, vol. 171(1), pages 186-208, October.
    5. YA. D. Sergeyev, 2000. "Efficient Strategy for Adaptive Partition of N-Dimensional Intervals in the Framework of Diagonal Algorithms," Journal of Optimization Theory and Applications, Springer, vol. 107(1), pages 145-168, October.
    6. William W. Cooper & Lawrence M. Seiford & Kaoru Tone, 2007. "Data Envelopment Analysis," Springer Books, Springer, edition 0, number 978-0-387-45283-8, December.
    7. Remigijus Paulavičius & Julius Žilinskas, 2014. "Simplicial Lipschitz optimization without the Lipschitz constant," Journal of Global Optimization, Springer, vol. 59(1), pages 23-40, May.
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    Cited by:

    1. Antanas Žilinskas & James Calvin, 2019. "Bi-objective decision making in global optimization based on statistical models," Journal of Global Optimization, Springer, vol. 74(4), pages 599-609, August.
    2. Cuicui Zheng & James Calvin & Craig Gotsman, 2021. "A DIRECT-type global optimization algorithm for image registration," Journal of Global Optimization, Springer, vol. 79(2), pages 431-445, February.

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