Constraint propagation with interval labels
Artificial Intelligence
Computing all solutions to polynomial systems using homotopy continuation
Applied Mathematics and Computation
ILPS '94 Proceedings of the 1994 International Symposium on Logic programming
Solving Polynomial Systems Using a Branch and Prune Approach
SIAM Journal on Numerical Analysis
Accelerating filtering techniques for numeric CSPs
Artificial Intelligence
Consistency techniques for numeric CSPs
IJCAI'93 Proceedings of the 13th international joint conference on Artifical intelligence - Volume 1
Algorithm 852: RealPaver: an interval solver using constraint satisfaction techniques
ACM Transactions on Mathematical Software (TOMS)
Safety verification of hybrid systems by constraint propagation-based abstraction refinement
ACM Transactions on Embedded Computing Systems (TECS)
Efficient interval partitioning-Local search collaboration for constraint satisfaction
Computers and Operations Research
ICOS: a branch and bound based solver for rigorous global optimization
Optimization Methods & Software - GLOBAL OPTIMIZATION
Enhancing numerical constraint propagation using multiple inclusion representations
Annals of Mathematics and Artificial Intelligence
Efficient pruning technique based on linear relaxations
COCOS'03 Proceedings of the Second international conference on Global Optimization and Constraint Satisfaction
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This paper introduces a new filtering algorithm for handling systems of quadratic equations and inequations. Such constraints are widely used to model distance relations in numerous application areas ranging from robotics to chemistry. Classical filtering algorithms are based upon local consistencies and thus, are unable to achieve a significant pruning of the domains of the variables occurring in quadratic constraints systems. The drawback of these approaches comes from the fact that the constraints are handled independently. We introduce here a global filtering algorithm that works on a tight linear relaxation of the quadratic constraints. First experimentations show that this new algorithm yields a much more effective pruning of the domains than local consistency filtering algorithms.