Revisiting the Upper Bounding Process in a Safe Branch and Bound Algorithm

  • Alexandre Goldsztejn
  • Yahia Lebbah
  • Claude Michel
  • Michel Rueher
Part of the Lecture Notes in Computer Science book series (LNCS, volume 5202)

Abstract

Finding feasible points for which the proof succeeds is a critical issue in safe Branch and Bound algorithms which handle continuous problems. In this paper, we introduce a new strategy to compute very accurate approximations of feasible points. This strategy takes advantage of the Newton method for under-constrained systems of equations and inequalities. More precisely, it exploits the optimal solution of a linear relaxation of the problem to compute efficiently a promising upper bound. First experiments on the Coconuts benchmarks demonstrate that this approach is very effective.

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References

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    Lebbah, Y., Michel, C., Rueher, M., Daney, D., Merlet, J.-P.: Efficient and safe global constraints for handling numerical constraint systems. SIAM Journal on Numerical Analysis 42(5), 2076–2097 (2004)CrossRefMathSciNetGoogle Scholar
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Copyright information

© Springer-Verlag Berlin Heidelberg 2008

Authors and Affiliations

  • Alexandre Goldsztejn
    • 1
  • Yahia Lebbah
    • 2
    • 3
  • Claude Michel
    • 3
  • Michel Rueher
    • 3
  1. 1.CNRS / Université de Nantes 2, rue de la HoussinièreNantesFrance
  2. 2.Université d’Oran Es-Senia B.P. 1524 EL-M’NaouarOranAlgeria
  3. 3.Université de Nice-Sophia Antipolis, I3S-CNRSSophia AntipolisFrance

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