In Figures 11 and 15 QN progress for Rosenbrock's and Beale's functions is shown. The QN code is taken from the package CONMIN of Shanno & Phua available in the NAG library. The QN paths are clearly more systematic than those associated with the gradient methods, following down the valley. Behavior of the limited- memory QN methods is essentially identical for these two-dimensional problems.
We refer the reader to additional papers [27,44] discussing state-of-the-art LMQN methods, along with practical schemes for initial scaling and for calculating each efficiently by exploiting the low-rank update procedure.