|Title||Efficient and Safe Global Constraints for Handling Numerical Constraint
|Author(s)|| David Daney, Yahia Lebbah, Jean-Pierre Merlet, Claude Michel, Michel Rueher|
|Text||accepted, Siam Journal on Numerical Analysis|
|Type||Technical Report, Misc|
|Abstract||Numerical constraint systems are often handled by branch and prune algorithms that combine splitting techniques, local consistencies and interval methods. This paper first recalls the principles of Quad, a global constraint that works on a tight and safe linear relaxation of|
quadratic subsystems of constraints. Then, it introduces a generalisation of Quad to polynomial constraint systems. It also introduces a method to get safe linear relaxations and shows how to compute safe bounds of the variables of the linear constraint system. Different linearisation techniques are investigated to limit the number of generated constraints. QuadSolver, a new branch and prune algorithm that combines Quad, local consistencies and interval methods is introduced. QuadSolver has been evaluated on a variety of benchmarks from kinematics, mechanics and robotics. On these benchmarks, it outperforms classical interval methods as well as CSP solvers and it compares well with state-of-the-art optimisation solvers.