Abstract
Interval-based methods can approximate all the real solutions of a system of equations and inequalities. The Box interval constraint propagation algorithm enforces Box consistency. Its main procedure BoxNarrow handles one function f corresponding to the revised constraint, and one variable x, replacing the other variables of f by their current intervals. This paper proposes an improved BoxNarrow procedure for narrowing the domain of x when f respects certain conditions. In particular, these conditions are fulfilled when f is polynomial. f is first symbolically rewritten into a new form g. A narrowing step is then run on the non-interval extremal functions that enclose the interval function g. The corresponding algorithm is described and validated on several numerical constraint systems.
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Trombettoni, G., Papegay, Y., Chabert, G., Pourtallier, O. (2010). A Box-Consistency Contractor Based on Extremal Functions. In: Cohen, D. (eds) Principles and Practice of Constraint Programming – CP 2010. CP 2010. Lecture Notes in Computer Science, vol 6308. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-15396-9_39
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DOI: https://doi.org/10.1007/978-3-642-15396-9_39
Publisher Name: Springer, Berlin, Heidelberg
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