Finding feasible points for which the proof succeeds is a critical issue in
safe Branch and Bound algorithms which handle continuous problems. In this
paper, we introduce a new strategy to compute very accurate approximations of
feasible points. This strategy takes advantage of the Newton method for
under-constrained systems of equations and inequalities. More precisely, it
exploits the optimal solution of a linear relaxation of the problem to compute
efficiently a promising upper bound. First experiments on the Coconuts
benchmarks demonstrate that this approach is very effective.Comment: Optimization, continuous domains, nonlinear constraint problems, safe
constraint based approaches; 14th International Conference on Principles and
Practice of Constraint Programming, Sydney : Australie (2008
