, Volume 15, Issue 2, pp 190–212 | Cite as

A new framework for sharp and efficient resolution of NCSP with manifolds of solutions

  • Alexandre Goldsztejn
  • Laurent Granvilliers


When numerical CSPs are used to solve systems of n equations with n variables, the preconditioned interval Newton operator plays two key roles: First it allows handling the n equations as a global constraint, hence achieving a powerful contraction. Second it can prove rigorously the existence of solutions. However, none of these advantages can be used for under-constrained systems of equations, which have manifolds of solutions. A new framework is proposed in this paper to extend the advantages of the preconditioned interval Newton to under-constrained systems of equations. This is achieved simply by allowing domains of the NCSP to be parallelepipeds, which generalize the boxes usually used as domains.


Interval analysis Branch and prune algorithm Preconditioned interval Newton Global constraint for under-constrained systems of equations 


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© Springer Science+Business Media, LLC 2009

Authors and Affiliations

  1. 1.CNRS, Laboratoire d’Informatique de Nantes AtlantiqueNantesFrance
  2. 2.Laboratoire d’Informatique de Nantes AtlantiqueUniversity of NantesNantesFrance

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