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A Comparison of Methods for the Computation of Affine Lower Bound Functions for Polynomials

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Global Optimization and Constraint Satisfaction (COCOS 2003)

Part of the book series: Lecture Notes in Computer Science ((LNTCS,volume 3478))

Abstract

In this paper the problem of finding an affine lower bound function for a multivariate polynomial is considered. For this task, a number of methods are presented, all based on the expansion of the given polynomial into Bernstein polynomials. Error bounds and numerical results for a series of randomly-generated polynomials are given.

This work has been supported by the German Research Council (DFG).

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Authors and Affiliations

  1. University of Applied Sciences / FH Konstanz, Postfach 100543, D-78405, Konstanz, Germany

    Jürgen Garloff & Andrew P. Smith

Authors
  1. Jürgen Garloff
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  2. Andrew P. Smith
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Editor information

Editors and Affiliations

  1. LINA, FRE CNRS 2729 – University of Nantes, 2, rue de la Houssinière, BP 92208, F-44322, Nantes cedex 3, France

    Christophe Jermann

  2. Institute for Mathematics, University Wien, Nordbergstr. 15, A-1090, Wien, Austria

    Arnold Neumaier

  3. Artificial Intelligence Laboratory, Swiss Federal Institute of Technology, Route J.-D. Colladon, Bat. INR, Office 235, CH-1015, Lausanne, Switzerland

    Djamila Sam

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© 2005 Springer-Verlag Berlin Heidelberg

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Garloff, J., Smith, A.P. (2005). A Comparison of Methods for the Computation of Affine Lower Bound Functions for Polynomials. In: Jermann, C., Neumaier, A., Sam, D. (eds) Global Optimization and Constraint Satisfaction. COCOS 2003. Lecture Notes in Computer Science, vol 3478. Springer, Berlin, Heidelberg. https://doi.org/10.1007/11425076_6

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  • DOI: https://doi.org/10.1007/11425076_6

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-540-26003-5

  • Online ISBN: 978-3-540-32041-8

  • eBook Packages: Computer ScienceComputer Science (R0)

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