The CLP( R ) language and system
ACM Transactions on Programming Languages and Systems (TOPLAS)
Naive solving of non-linear constraints
Constraint logic programming
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
Symbolic-interval cooperation in constraint programming
Proceedings of the 2001 international symposium on Symbolic and algebraic computation
CLIP: A CLP(Intervals) Dialect for Metalevel Constraint Solving
PADL '00 Proceedings of the Second International Workshop on Practical Aspects of Declarative Languages
Solving Nonlinear Systems by Constraint Inversion and Interval Arithmetic
AISC '00 Revised Papers from the International Conference on Artificial Intelligence and Symbolic Computation
Numerica: a modeling language for global optimization
IJCAI'97 Proceedings of the Fifteenth international joint conference on Artifical intelligence - Volume 2
Algorithm 852: RealPaver: an interval solver using constraint satisfaction techniques
ACM Transactions on Mathematical Software (TOMS)
Efficient interval partitioning-Local search collaboration for constraint satisfaction
Computers and Operations Research
Exploiting Common Subexpressions in Numerical CSPs
CP '08 Proceedings of the 14th international conference on Principles and Practice of Constraint Programming
| Hi-index | 0.00 |
The solving engines of most of constraint programming systems use interval-based consistency techniques to process nonlinear systems over the reals. However, few symbolic-interval cooperative solvers are implemented. The challenge is twofold: control of the amount of symbolic computations, and prediction of the accuracy of interval computations over transformed systems.In this paper, we introduce a new symbolic pre-processing for interval branch-and-prune algorithms based on box consistency. The symbolic algorithm computes a linear relaxation by abstraction of the nonlinear terms. The resulting rectangular linear system is processed by Gaussian elimination. Control strategies of the densification of systems during elimination are devised. Three scalable problems known to be hard for box consistency are efficiently solved.