Abstract
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.
Access provided by Autonomous University of Puebla. Download to read the full chapter text
Chapter PDF
Similar content being viewed by others
Keywords
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.
References
Collins, G.: Quantifier elimination by cylindrical algebraic decomposition–twenty years of progress. In: Quantifier Elimination and Cylindrical Algebraic Decomposition, pp. 8–23 (1998)
Ratschan, S.: Uncertainty propagation in heterogeneous algebras for approximate quantified constraint solving. Journal of Universal Computer Science 6(9), 861–880 (2000)
Shary, S.: A new technique in systems analysis under interval uncertainty and ambiguity. Reliable computing 8, 321–418 (2002)
Goldsztejn, A.: A Right-Preconditioning Process for the Formal-Algebraic Approach to Inner and Outer Estimation of AE-solution Sets. Reliable Computing 11(6), 443–478 (2005)
Herrero, P., Jaulin, L., Vehi, J., Sainz, M.: Inner and outer approximation of the polar diagram of a sailboat. In: van Beek, P. (ed.) CP 2005. LNCS, vol. 3709. Springer, Heidelberg (2005)
Goldsztejn, A.: A branch and prune algorithm for the approximation of non-linear ae-solution sets. In: Proceedings of the 21st ACM Symposium on Applied Computing track Reliable Computations and their Applications (SAC 2006), Dijon, France (April 2006)
Khalil, H.: Nonlinear Systems, 3rd edn. Prentice Hall, Englewood Cliffs (2002)
Reboulet, C.: Modélisation des robots parallèles. In: Boissonat, J.D., Faverjon, B., Merlet, J.P. (eds.) Techniques de la robotique, architecture et commande. Hermès, Paris, France, pp. 257–284 (1988)
Moore, R.: Interval analysis. Prentice-Hall, Englewood Cliffs (1966)
Benhamou, F., Older, W.: Applying Interval Arithmetic to Real, Integer and Boolean Constraints. Journal of Logic Programming 32(1), 1–24 (1997)
Haug, E., Luh, C., Adkins, F., Wang, J.: Numerical algorithms for mapping boundaries of manipulator workspaces. ASME Journal of Mechanical Design 118, 228–234 (1996)
Jaulin, L., Kieffer, M., Didrit, O., Walter, E.: Applied Interval Analysis with Examples in Parameter and State Estimation. In: Robust Control and Robotics. Springer, Heidelberg (2001)
Lebbah, Y., Michel, C., Rueher, M., Daney, D., Merlet, J.: Efficient and Safe Global Constraints for handling Numerical Constraint Systems. SIAM Journal on Numerical Analysis 42(5), 2076–2097 (2005)
Neumaier, A.: Interval Methods for Systems of Equations. Cambridge Univ. Press, Cambridge (1990)
Goldsztejn, A., Jaulin, L.: Inner Approximation of the Range of Vector-Valued Functions to Reliable Computing (submitted)
Author information
Authors and Affiliations
Editor information
Editors and Affiliations
Rights and permissions
Copyright information
© 2006 Springer-Verlag Berlin Heidelberg
About this paper
Cite this paper
Goldsztejn, A., Jaulin, L. (2006). Inner and Outer Approximations of Existentially Quantified Equality Constraints. In: Benhamou, F. (eds) Principles and Practice of Constraint Programming - CP 2006. CP 2006. Lecture Notes in Computer Science, vol 4204. Springer, Berlin, Heidelberg. https://doi.org/10.1007/11889205_16
Download citation
DOI: https://doi.org/10.1007/11889205_16
Publisher Name: Springer, Berlin, Heidelberg
Print ISBN: 978-3-540-46267-5
Online ISBN: 978-3-540-46268-2
eBook Packages: Computer ScienceComputer Science (R0)