An efficient and safe framework for solving optimization problems
Journal of Computational and Applied Mathematics - Special issue: Scientific computing, computer arithmetic, and validated numerics (SCAN 2004)
Using constraint techniques for a safe and fast implementation of optimality-based reduction
Proceedings of the 2007 ACM symposium on Applied computing
Revisiting the Upper Bounding Process in a Safe Branch and Bound Algorithm
CP '08 Proceedings of the 14th international conference on Principles and Practice of Constraint Programming
ICOS: a branch and bound based solver for rigorous global optimization
Optimization Methods & Software - GLOBAL OPTIMIZATION
Optimization Methods & Software - GLOBAL OPTIMIZATION
A linear relaxation technique for the position analysis of multiloop linkages
IEEE Transactions on Robotics
Filtering numerical CSPs using well-constrained subsystems
CP'09 Proceedings of the 15th international conference on Principles and practice of constraint programming
A safe and flexible CP-based approach for velocity tuning problems
CP'10 Proceedings of the 16th international conference on Principles and practice of constraint programming
Inner and outer approximations of existentially quantified equality constraints
CP'06 Proceedings of the 12th international conference on Principles and Practice of Constraint Programming
When interval analysis helps inter-block backtracking
CP'06 Proceedings of the 12th international conference on Principles and Practice of Constraint Programming
Finding all solutions of separable systems of piecewise-linear equations using integer programming
Journal of Computational and Applied Mathematics
ICN-RE: redundancy elimination for information-centric networking
Proceedings of the second edition of the ICN workshop on Information-centric networking
FDCC: a combined approach for solving constraints over finite domains and arrays
CPAIOR'12 Proceedings of the 9th international conference on Integration of AI and OR Techniques in Constraint Programming for Combinatorial Optimization Problems
Boosting local consistency algorithms over floating-point numbers
CP'12 Proceedings of the 18th international conference on Principles and Practice of Constraint Programming
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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 {\tt Quad}, a global constraint that works on a tight and safe linear relaxation of quadratic subsystems of constraints. Then, it introduces a generalization of {\tt 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 linearization techniques are investigated to limit the number of generated constraints. {\tt QuadSolver}, a new branch and prune algorithm that combines {\tt Quad}, local consistencies, and interval methods, is introduced. {\tt 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 constraint satisfaction problem solvers and it compares well with state-of-the-art optimization solvers.