A Box-Consistency Contractor Based on Extremal Functions

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. 1 Motivation Interval-based solvers can solve systems of numerical constraints (i.e., nonlinear equations or inequalities over the reals). Their reliability and increasing performance make t...

• Type: Journal
• Year: 2010
• Where: CP
• Authors: Gilles Trombettoni, Yves Papegay, Gilles Chabert, Odile Pourtallier
• Keywords: Algorithms, Artificial Intelligence, CP 2010, Interval Constraint Propagation, Numerical Constraint