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Acceleration of Global Search by Implementing Dual Estimates for Lipschitz Constant

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Numerical Computations: Theory and Algorithms (NUMTA 2019)

Part of the book series: Lecture Notes in Computer Science ((LNTCS,volume 11974))

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Abstract

The paper considers global optimization problems with a black-box objective function satisfying the Lipschitz condition. Efficient algorithms for this class of problems require reliable estimates of the Lipschitz constant to be introduced. Various approaches have been proposed to take into account both global and local properties of the objective function. In particular, algorithms using local estimates of the Lipschitz constant have shown their potential. The new approach presented in this paper is based on simultaneous use of two estimates: one is substantially larger than the other. The larger estimate ensures global convergence and the smaller one reduces the total number of trials needed to find the global optimizer. Results of numerical experiments on the random sample of multidimensional functions demonstrate the efficiency of the approach proposed by the authors.

This research was supported by the Russian Science Foundation, project No. 16-11-10150.

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Authors and Affiliations

  1. Lobachevsky State University of Nizhni Novgorod, Nizhny Novgorod, Russia

    Roman Strongin, Konstantin Barkalov & Semen Bevzuk

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  1. Roman Strongin
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  2. Konstantin Barkalov
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  3. Semen Bevzuk
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Correspondence to Konstantin Barkalov .

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Editors and Affiliations

  1. University of Calabria, Rende, Italy

    Yaroslav D. Sergeyev

  2. University of Calabria, Rende, Italy

    Dmitri E. Kvasov

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Strongin, R., Barkalov, K., Bevzuk, S. (2020). Acceleration of Global Search by Implementing Dual Estimates for Lipschitz Constant. In: Sergeyev, Y., Kvasov, D. (eds) Numerical Computations: Theory and Algorithms. NUMTA 2019. Lecture Notes in Computer Science(), vol 11974. Springer, Cham. https://doi.org/10.1007/978-3-030-40616-5_46

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  • DOI: https://doi.org/10.1007/978-3-030-40616-5_46

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  • Online ISBN: 978-3-030-40616-5

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