Transformations enabling to construct limited-memory Broyden class methods

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.

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Technical report No. V 1037, Institute of Computer Science, Pod Vodarenskou Vezi 2, 18207 Praha 8. December 2008

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