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Derivative-Free Local Tuning and Local Improvement Techniques Embedded in the Univariate Global Optimization

Author

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  • Yaroslav D. Sergeyev

    (Università della Calabria
    Lobachevsky State University of Nizhni Novgorod)

  • Marat S. Mukhametzhanov

    (Università della Calabria
    Lobachevsky State University of Nizhni Novgorod)

  • Dmitri E. Kvasov

    (Università della Calabria
    Lobachevsky State University of Nizhni Novgorod)

  • Daniela Lera

    (Università di Cagliari)

Abstract

Geometric and information frameworks for constructing global optimization algorithms are considered, and several new ideas to speed up the search are proposed. The accelerated global optimization methods automatically realize a local behavior in the promising subregions without the necessity to stop the global optimization procedure. Moreover, all the trials executed during the local phases are used also in the course of the global ones. The resulting geometric and information global optimization methods have a similar structure, and a smart mixture of new and traditional computational steps leads to 22 different global optimization algorithms. All of them are studied and numerically compared on three test sets including 120 benchmark functions and 4 applied problems.

Suggested Citation

  • 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.
    • Handle: RePEc:spr:joptap:v:171:y:2016:i:1:d:10.1007_s10957-016-0947-5
    DOI: 10.1007/s10957-016-0947-5
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    References listed on IDEAS

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    1. Daniela Lera & Yaroslav Sergeyev, 2010. "An information global minimization algorithm using the local improvement technique," Journal of Global Optimization, Springer, vol. 48(1), pages 99-112, September.
    2. Jonathan Gillard & Anatoly Zhigljavsky, 2013. "Optimization challenges in the structured low rank approximation problem," Journal of Global Optimization, Springer, vol. 57(3), pages 733-751, November.
    3. 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.
    4. 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.
    5. James M. Calvin & Yvonne Chen & Antanas Žilinskas, 2012. "An Adaptive Univariate Global Optimization Algorithm and Its Convergence Rate for Twice Continuously Differentiable Functions," Journal of Optimization Theory and Applications, Springer, vol. 155(2), pages 628-636, November.
    6. Anatoly Zhigljavsky & Antanas Žilinskas, 2008. "Stochastic Global Optimization," Springer Optimization and Its Applications, Springer, number 978-0-387-74740-8, December.
    7. Hamacher, Kay, 2005. "On stochastic global optimization of one-dimensional functions," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 354(C), pages 547-557.
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    1. Sergeyev, Yaroslav D. & Kvasov, Dmitri E. & Mukhametzhanov, Marat S., 2017. "Operational zones for comparing metaheuristic and deterministic one-dimensional global optimization algorithms," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 141(C), pages 96-109.
    2. Anis Fradi & Chafik Samir & Ines Adouani, 2024. "A New Bayesian Approach to Global Optimization on Parametrized Surfaces in $$\mathbb {R}^{3}$$ R 3," Journal of Optimization Theory and Applications, Springer, vol. 202(3), pages 1077-1100, September.
    3. R. Cavoretto & A. Rossi & M. S. Mukhametzhanov & Ya. D. Sergeyev, 2021. "On the search of the shape parameter in radial basis functions using univariate global optimization methods," Journal of Global Optimization, Springer, vol. 79(2), pages 305-327, February.
    4. Grishagin, Vladimir & Israfilov, Ruslan & Sergeyev, Yaroslav, 2018. "Convergence conditions and numerical comparison of global optimization methods based on dimensionality reduction schemes," Applied Mathematics and Computation, Elsevier, vol. 318(C), pages 270-280.
    5. Falcone, Alberto & Garro, Alfredo & Mukhametzhanov, Marat S. & Sergeyev, Yaroslav D., 2021. "A Simulink-based software solution using the Infinity Computer methodology for higher order differentiation," Applied Mathematics and Computation, Elsevier, vol. 409(C).
    6. 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.
    7. Renato Bruni & Fabio Celani, 2019. "Combining Global and Local Strategies to Optimize Parameters in Magnetic Spacecraft Control via Attitude Feedback," Journal of Optimization Theory and Applications, Springer, vol. 181(3), pages 997-1014, June.
    8. Kvasov, Dmitri E. & Mukhametzhanov, Marat S., 2018. "Metaheuristic vs. deterministic global optimization algorithms: The univariate case," Applied Mathematics and Computation, Elsevier, vol. 318(C), pages 245-259.

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