Nonlinear control system design by quantifier elimination
Journal of Symbolic Computation - Special issue: applications of quantifier elimination
Interval constraint solving for camera control and motion planning
ACM Transactions on Computational Logic (TOCL)
An efficient algorithm for a sharp approximation of universally quantified inequalities
Proceedings of the 2008 ACM symposium on Applied computing
A New Framework for Sharp and Efficient Resolution of NCSP with Manifolds of Solutions
CP '08 Proceedings of the 14th international conference on Principles and Practice of Constraint Programming
Artificial Intelligence
Generalized interval projection: a new technique for consistent domain extension
IJCAI'07 Proceedings of the 20th international joint conference on Artifical intelligence
Inner and outer approximations of existentially quantified equality constraints
CP'06 Proceedings of the 12th international conference on Principles and Practice of Constraint Programming
A branch and prune algorithm for the computation of generalized aspects of parallel robots
CP'12 Proceedings of the 18th international conference on Principles and Practice of Constraint Programming
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Non-linear AE-solution sets are a special case of parametric systems of equations where universally quantified parameters appear first. They allow to model many practical situations. A new branch and prune algorithm dedicated to the approximation of non-linear AE-solution sets is proposed. It is based on a new generalized interval (intervals whose bounds are not constrained to be ordered) parametric Hansen-Sengupta operator. In spite of some restrictions on the form of the AE-solution set which can be approximated, it allows to solve problems which were before out of reach of previous numerical methods. Some promising experimentations are presented.