Résolution de problèmes non linéaires avec continuum de solutions

We address the issue of constructing concise inner and outer approximations of the complete solution set for non-linear constraint satisfaction problems (CSPs). Most of the working complete solvers for numerical CSPs are designed to delivering point-wise solutions with an arbitrary accuracy. This works generally well for systems with isolated solutions but less well when there is a continuum of feasible points (e.g. under-constrained problems, problems with inequalities). In many practical applications, such large sets of solutions express equally relevant alternatives which need to be identified as completely as possible. In this paper, we propose a technique for constructing inner and outer approximations as unions of interval boxes. The proposed technique combines a new splitting strategy with the extreme vertex representation of orthogonal polyhedra [BOU 00], as defined in computational geometry. This allows for compacting the representation of the approximations and improves efficiency. MOTS-CLÉS : Satisfaction de contraintes numérique, continuum de solution, approximations