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Global Optimization Method with Numerically Calculated Function Derivatives

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Advances in Optimization and Applications (OPTIMA 2020)

Part of the book series: Communications in Computer and Information Science ((CCIS,volume 1340))

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Abstract

The paper proposes a method for solving computationally time-consuming multidimensional global optimization problems. The developed method combines the use of a nested dimensional reduction scheme and numerical estimates of the objective function derivatives. Derivatives significantly reduce the cost of solving global optimization problems, however, the use of a nested scheme can lead to the fact that the derivatives of the reduced function become discontinuous. Typical global optimization methods are highly dependent on the continuity of the objective function. Thus, to use derivatives in combination with a nested scheme, an optimization method is required that can work with discontinuous functions. The paper discusses the corresponding method, as well as the results of numerical experiments in which such an optimization scheme is compared with other known methods.

Supported by Russian Foundation for Basic Research (grant 19-07-00242).

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Authors and Affiliations

  1. Lobachevsky State University of Nizhny Novgorod, Nizhny Novgorod, Russian Federation

    Victor Gergel & Alexander Sysoyev

Authors
  1. Victor Gergel
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  2. Alexander Sysoyev
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Correspondence to Alexander Sysoyev .

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Editors and Affiliations

  1. FRC CSC RAS, Moscow, Russia

    Nicholas Olenev

  2. FRC CSC RAS, Moscow, Russia

    Yuri Evtushenko

  3. Krasovsky Institute of Mathematics and Mechanics, Yekaterinburg, Russia

    Michael Khachay

  4. FRC CSC RAS, Moscow, Russia

    Vlasta Malkova

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Gergel, V., Sysoyev, A. (2020). Global Optimization Method with Numerically Calculated Function Derivatives. In: Olenev, N., Evtushenko, Y., Khachay, M., Malkova, V. (eds) Advances in Optimization and Applications. OPTIMA 2020. Communications in Computer and Information Science, vol 1340. Springer, Cham. https://doi.org/10.1007/978-3-030-65739-0_1

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  • DOI: https://doi.org/10.1007/978-3-030-65739-0_1

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  • Publisher Name: Springer, Cham

  • Print ISBN: 978-3-030-65738-3

  • Online ISBN: 978-3-030-65739-0

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