The last problem which must be considered is that we can never reach the local minimum. Often it has been said that refinement was continued until convergence at the local minimum. Even in a perfect case, where our refinement residual was quadratic, both Conjugate Gradient and Conjugate Direction would require n cycles where n is at least four times the number of atoms in the model. No one has ever ran that many cycles.
This means that no one has ever been ``trapped in a local minimum''. They have never reached a local minimum.