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Handbook of Global Optimization pp 751–828Cite as

Interval Methods

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Part of the book series: Nonconvex Optimization and Its Applications ((NOIA,volume 2))

Abstract

An introduction to the interval arithmetic tools and basic methods that can be used to solve global optimization problems are presented. These tools are applicable both to unconstrained and constrained as well as to nonsmooth optimization or to problems over unbounded domains. We also emphasize the role of bisections and attempts to find the right bisections when solving the problem computationally since almost all interval based global optimization algorithms use branch-and-bound principles where the problem domain is bisected iteratively and since the research on bisection strategies has made significant progress during the last decade.

Thanks are due to the National Science and Engineering Research Council of Canada for financial support.

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Author information

Authors and Affiliations

  1. Mathematisches Institut, Universität Düsseldorf, 4 Düsseldorf 1, Universitätstrasse 1, 4 Düsseldorf 1, Germany

    Helmut Ratschek

  2. Department of Computer Science, The University of Calgary, 2500 University Drive, N. W., T2N-1N4, Calgary, Alberta, Canada

    Jon Rokne

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  1. Helmut Ratschek
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  2. Jon Rokne
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Editors and Affiliations

  1. Department of Mathematics, University of Trier, Trier, Germany

    Reiner Horst

  2. Department of Industrial and Systems Engineering, University of Florida, Gainesville, Florida, USA

    Panos M. Pardalos

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Ratschek, H., Rokne, J. (1995). Interval Methods. In: Horst, R., Pardalos, P.M. (eds) Handbook of Global Optimization. Nonconvex Optimization and Its Applications, vol 2. Springer, Boston, MA. https://doi.org/10.1007/978-1-4615-2025-2_14

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  • DOI: https://doi.org/10.1007/978-1-4615-2025-2_14

  • Publisher Name: Springer, Boston, MA

  • Print ISBN: 978-1-4613-5838-1

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