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International Conference on Optimization and Applications

OPTIMA 2018: Optimization and Applications pp 170–185Cite as

Piecewise Linear Bounding Functions for Univariate Global Optimization

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Part of the book series: Communications in Computer and Information Science ((CCIS,volume 974))

Abstract

The paper addresses the problem of constructing lower and upper bounding functions for univariate functions. This problem is of a crucial importance in global optimization where such bounds are used by deterministic methods to reduce the search area. It should be noted that bounding functions are expected to be relatively easy to construct and manipulate with. We propose to use piecewise linear estimators for bounding univariate functions. The rules proposed in the paper enable an automated synthesis of lower and upper bounds from the function’s expression in an algebraic form. Numerical examples presented in the paper demonstrate the high accuracy of the proposed bounds.

The reported study was funded by RFBR according to the research project 17-07-00510.

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Author information

Authors and Affiliations

  1. Melentiev Energy Systems Institute of Siberian Branch of the Russian Academy of Sciences, Lermontov st.,130, Irkutsk, 664033, Russia

    Oleg Khamisov

  2. Dorodnicyn Computing Centre, FRC CSC RAS, Vavilov st. 40, Moscow, Russia

    Mikhail Posypkin & Alexander Usov

  3. Moscow Institute of Physics and Technology, Institutskiy Pereulok, 9 Dolgoprudny, Russia

    Mikhail Posypkin

  4. Institute for Information Transmission Problems RAS, Bolshoy Karetny per. 19, build. 1, Moscow, 127051, Russia

    Mikhail Posypkin

Authors
  1. Oleg Khamisov
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  2. Mikhail Posypkin
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  3. Alexander Usov
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Corresponding author

Correspondence to Alexander Usov .

Editor information

Editors and Affiliations

  1. FRC CSC RAS, Dorodnitsyn Computing Centre, Moscow, Russia

    Yury Evtushenko

  2. University of Montenegro, Podgorica, Montenegro

    Milojica Jaćimović

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

    Michael Khachay

  4. Sobolev Institute of Mathematics, Siberian Branch of the Russian Academy of Sciences, Novosibirsk, Russia

    Yury Kochetov

  5. FRC CSC RAS, Dorodnitsyn Computing Centre, Moscow, Russia

    Vlasta Malkova

  6. FRC CSC RAS, Dorodnitsyn Computing Centre, Moscow, Russia

    Mikhail Posypkin

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Khamisov, O., Posypkin, M., Usov, A. (2019). Piecewise Linear Bounding Functions for Univariate Global Optimization. In: Evtushenko, Y., Jaćimović, M., Khachay, M., Kochetov, Y., Malkova, V., Posypkin, M. (eds) Optimization and Applications. OPTIMA 2018. Communications in Computer and Information Science, vol 974. Springer, Cham. https://doi.org/10.1007/978-3-030-10934-9_13

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  • DOI: https://doi.org/10.1007/978-3-030-10934-9_13

  • Published:

  • Publisher Name: Springer, Cham

  • Print ISBN: 978-3-030-10933-2

  • Online ISBN: 978-3-030-10934-9

  • eBook Packages: Computer ScienceComputer Science (R0)

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