Solving Existentially Quantified Constraints with One Equality and Arbitrarily Many Inequalities

  • Stefan Ratschan
Conference paper
Part of the Lecture Notes in Computer Science book series (LNCS, volume 2833)


This paper contains the first algorithm that can solve disjunctions of constraints of the form \(\exists{y}\!\in\! B \; [ f=0 \;\wedge\; g_1\geq 0\wedge\dots\wedge g_k\geq 0 ]\) in free variables x, terminating for all cases when this results in a numerically well-posed problem. Here the only assumption on the terms f, g 1,..., g n is the existence of a pruning function, as given by the usual constraint propagation algorithms or by interval evaluation. The paper discusses the application of an implementation of the resulting algorithm on problems from control engineering, parameter estimation, and computational geometry.


Constraint Programming Symbolic Computation Bounded Constraint Positive Degree Pruning Algorithm 


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Copyright information

© Springer-Verlag Berlin Heidelberg 2003

Authors and Affiliations

  • Stefan Ratschan
    • 1
  1. 1.Max-Planck-Institut für InformatikSaarbrückenGermany

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