The Broyden class of quasi-Newton updates for inverse Hessian approximation are transformed to the formal BFGS update, which makes possible to generalize the well-known Nocedal method based on the Strang recurrences to the scaled limited-memory Broyden family, using the same number of stored vectors as for the limited-memory BFGS method. Two variants are given, the simpler of them does not require any additional matrix by vector multiplications. Numerical results indicate that this approach can save computational time.
Technical report No. V 1037, Institute of Computer Science, Pod Vodarenskou Vezi 2, 18207 Praha 8. December 2008