Inner and Outer Approximations of Existentially Quantified Equality Constraints

  • Alexandre Goldsztejn
  • Luc Jaulin
Part of the Lecture Notes in Computer Science book series (LNCS, volume 4204)


We propose a branch and prune algorithm that is able to compute inner and outer approximations of the solution set of an existentially quantified constraint where existential parameters are shared between several equations. While other techniques that handle such constraints need some preliminary formal simplification of the problem or only work on simpler special cases, our algorithm is the first pure numerical algorithm that can approximate the solution set of such constraints in the general case. Hence this new algorithm allows computing inner approximations that were out of reach until today.


Singular Vector Interval Analysis Interval Arithmetic Outer Approximation Constraint Graph 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.


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Copyright information

© Springer-Verlag Berlin Heidelberg 2006

Authors and Affiliations

  • Alexandre Goldsztejn
    • 1
  • Luc Jaulin
    • 2
  1. 1.Computer Science DepartmentUniversity of Central ArkansasConway, ArkansasUSA
  2. 2.Luc Jaulin: E3I2ENSIETABrest

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