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Developments in Global Optimization pp 109–119Cite as

Interval and Bounding Hessians

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Part of the book series: Nonconvex Optimization and Its Applications ((NOIA,volume 18))

Abstract

Bounding Hessians are defined and an O(n 2) method of obtaining optimal bounding Hessians from interval Hessians is presented. They are applied to a framework of an adaptive second derivative covering method for global optimization, which is presented here. Also, bounding Hessians can be used for reformulation of very general global optimization problems into several useful forms for which there are existing algorithms.

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References

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Author information

Authors and Affiliations

  1. Department of Mathematics and Statistics, University of Canterbury, Christchurch, New Zealand

    Chris Stephens

Authors
  1. Chris Stephens
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Editor information

Editors and Affiliations

  1. University of Vienna, Vienna, Austria

    Immanuel M. Bomze

  2. József Attila University, Szeged, Hungary

    Tibor Csendes

  3. University of Trier, Trier, Germany

    Reiner Horst

  4. University of Florida, Gainesville, Florida, USA

    Panos M. Pardalos

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© 1997 Springer Science+Business Media Dordrecht

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Stephens, C. (1997). Interval and Bounding Hessians. In: Bomze, I.M., Csendes, T., Horst, R., Pardalos, P.M. (eds) Developments in Global Optimization. Nonconvex Optimization and Its Applications, vol 18. Springer, Boston, MA. https://doi.org/10.1007/978-1-4757-2600-8_7

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  • DOI: https://doi.org/10.1007/978-1-4757-2600-8_7

  • Publisher Name: Springer, Boston, MA

  • Print ISBN: 978-1-4419-4768-0

  • Online ISBN: 978-1-4757-2600-8

  • eBook Packages: Springer Book Archive

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