Is the Hessian used in non linear JuMP?

Thanks for the reply @odow.

Just to make it a bit more clear, if I have a problem of the type:
@NLobjective(mode, Min, J)

@NLconstraint(model, J==my_NL_fun_with_autodiff(x))

will that use the hessian? (sorry about insisting, but I know that for my specific problem, quasi-newton does not work well enough)