Inner and Outer Approximations of Existentially Quantified Equality Constraints

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.

• Type: Conference
• Year: 2006
• Where: CP
• Authors: Alexandre Goldsztejn, Luc Jaulin
• Keywords: Algorithm, Artificial Intelligence, CP 2006, Prune Algorithm, Pure Numerical Algorithm