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• W2049953405 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 {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." @default.
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• W2049953405 date "2005-01-01" @default.
• W2049953405 modified "2023-09-26" @default.
• W2049953405 title "Efficient and Safe Global Constraints for Handling Numerical Constraint Systems" @default.
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• W2049953405 doi "https://doi.org/10.1137/s0036142903436174" @default.
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