Hi 
the problem is most likely the square root terms in your model equations which is not defined for negative values (and its derivative close to zero can also cause troubles). Even if the solution is well-defined, you need to ensure that the model provides reasonable values also for intermediate SQP iterates, e.g. the expression \sqrt{x^2 + \epsilon} with \epsilon > 0 works fine as the term inside the square root will always be positive independent of the value of x.
Could you reformulate your model in such a way that the square root function will only ever be evaluated at positive values?
Best, Katrin