What every computer scientist should know about floating-point arithmetic
ACM Computing Surveys (CSUR)
Estimation theory for nonlinear models and set membership uncertainty
Automatica (Journal of IFAC)
Minimizing conflicts: a heuristic repair method for constraint satisfaction and scheduling problems
Artificial Intelligence - Special volume on constraint-based reasoning
Lisp and Symbolic Computation
Guaranteed nonlinear parameter estimation from bounded-error data via interval analysis
Mathematics and Computers in Simulation
ILPS '94 Proceedings of the 1994 International Symposium on Logic programming
Revising hull and box consistency
Proceedings of the 1999 international conference on Logic programming
Extending Consistent Domains of Numeric CSP
IJCAI '99 Proceedings of the Sixteenth International Joint Conference on Artificial Intelligence
Range-Based Algorithm for Max-CSP
CP '02 Proceedings of the 8th International Conference on Principles and Practice of Constraint Programming
Performance of Various Computers Using Standard Linear Equations Software
Performance of Various Computers Using Standard Linear Equations Software
Interval constraint solving for camera control and motion planning
ACM Transactions on Computational Logic (TOCL)
Consistency techniques for numeric CSPs
IJCAI'93 Proceedings of the 13th international joint conference on Artifical intelligence - Volume 1
Counting the number of connected components of a set and its application to robotics
PARA'04 Proceedings of the 7th international conference on Applied Parallel Computing: state of the Art in Scientific Computing
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The Constraint Satisfaction Problem (CSP) framework allows users to define problems in a declarative way, quite independently from the solving process. However, when the problem is over-constrained, the answer "no solution" is generally unsatisfactory. A Max-CSP $\mathcal{P}_m = \langle V, \textbf{D}, C \rangle$ is a triple defining a constraint problem whose solutions maximize the number of satisfied constraints. In this paper, we focus on numerical CSPs, which are defined on real variables represented as floating point intervals and which constraints are numerical relations defined in intension. Solving such a problem (i.e., exactly characterizing its solution set) is generally undecidable and thus consists in providing approximations. We propose a Branch and Bound algorithm that provides under and over approximations of a solution set that maximize the maximum number ${m_{\mathcal P}}$ of satisfied constraints. The technique is applied on three numeric applications and provides promising results.