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Models and Algorithms for Global Optimization pp 97–108Cite as

A Survey of Methods for the Estimation Ranges of Functions Using Interval Arithmetic

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Part of the book series: Optimization and Its Applications ((SOIA,volume 4))

Abstract

Interval arithmetic is a valuable tool in numerical analysis and modeling. Interval arithmetic operates with intervals defined by two real numbers and produces intervals containing all possible results of corresponding real operations with real numbers from each interval. An interval function can be constructed replacing the usual arithmetic operations by interval arithmetic operations in the algorithm calculating values of functions. An interval value of a function can be evaluated using the interval function with interval arguments and determines the lower and upper bounds for the function in the region defined by the vector of interval arguments.

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Author information

Authors and Affiliations

  1. Institute of Mathematics and Informatics, Akademijos 4, LT-08663, Vilnius, Lithuania

    Julius Žilinskas

  2. Centre for Process Systems Engineering, Department of Chemical Engineering, University College London, Torrington Place, London, WC1E 7JE, UK

    Ian David Lockhart Bogle

Authors
  1. Julius Žilinskas
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  2. Ian David Lockhart Bogle
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Editor information

Editors and Affiliations

  1. Åbo Akademi University, Åbo, Finland

    Aimo Törn

  2. Institute of Mathematics and Informatics, Vilnius, Lithuania

    Julius Žilinskas

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Žilinskas, J., Bogle, I.D.L. (2007). A Survey of Methods for the Estimation Ranges of Functions Using Interval Arithmetic. In: Törn, A., Žilinskas, J. (eds) Models and Algorithms for Global Optimization. Optimization and Its Applications, vol 4. Springer, Boston, MA. https://doi.org/10.1007/978-0-387-36721-7_6

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