Solvers

Chapter 4 presented contractors that make it possible to contain a compact set $${\Bbb S}$$ defined by non-linear equations and inequalities in a box. Although the results are guaranteed, the accuracy with which $${\Bbb S}$$ is characterized is not under control. On the other hand, bisection allows accuracy to be controlled, but causes exponential complexity. Bisection should therefore be avoided as much as possible when the number of variables is high, in an attempt to escape the curse of dimensionality. This is why, in our opinion, when many variables are involved bisection should be used as a last resort, only when all available contractors have failed. A decision may then have to be taken as to which variable domains should be bisected.