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A revised algorithm is given for unconstrained optimization using quasi-Newton methods. The method is based on recurring the factorization of an approximation to the Hessian matrix. Knowledge of this factorization allows greater flexibility when choosing the direction of search while minimizing the adverse effects of rounding error. The control of rounding error is particularly important when analytical derivatives are unavailable, and a modification of the algorithm to accept finite-difference approximations to the derivatives is given.
Gill et al. (Sat,) studied this question.