Ignored constraints on non linear problem

Hi,

Modelling a binary variable as x*(x-1) often makes the problem impossible to solve with a local solver as it will get stuck in a locally infeasible solution; probably the reason why the solution appears to be infeasible. There is a similar problem with using the round function, which will also make the problem non-differentiable.

At the technology level, Xpress approaches a binary restriction x in {0,1} fundamentally differently then x*(x-1) = 0: the first one is treated as a MIP entity that will most likely be branched on (unless it can be fixed by implication or it happens to be 0 or 1 at the local optimal solutions) while the nonlinear constraint version is treated as a traditional problem constraint (which is not branched on in a local solver if it is converged to an infeasible point).