Although popular, quasi-Newton methods may converge to a stationary point that is not necessarily a local or global maximum,See theorem 10.1 in but rather a local minimum or a saddle point. Therefore, it is important to assess the validity of the obtained solution to the likelihood equations, by verifying that the Hessian, evaluated at the solution, is both negative definite and well-conditioned.
Although popular quasi-Newton methods may converge to a stationary point that is not necessarily a local or global maximum,See theorem 10.1 in but rather a local minimum or a saddle point Therefore, it is important to assess the validity of the obtained solution to the likelihood equations, by verifying that the Hessian, evaluated at the solution, is both negative definite and well-conditioned.