Piecewise Linear Bounding Functions for Univariate Global Optimization

  • Oleg Khamisov
  • Mikhail Posypkin
  • Alexander UsovEmail author
Conference paper
Part of the Communications in Computer and Information Science book series (CCIS, volume 974)


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.


Univariate global optimization Piecewise linear functions Estimators Deterministic methods 


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© Springer Nature Switzerland AG 2019

Authors and Affiliations

  1. 1.Melentiev Energy Systems Institute of Siberian Branch of the Russian Academy of SciencesIrkutskRussia
  2. 2.Dorodnicyn Computing Centre, FRC CSC RASMoscowRussia
  3. 3.Moscow Institute of Physics and TechnologyInstitutskiy Pereulok9 DolgoprudnyRussia
  4. 4.Institute for Information Transmission Problems RASMoscowRussia

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