Computational experiments with scaled initial Hessian approximation for the Broyden family methods

In this paper we consider two alternative choices for the factor used to scale the initial Hessian approximation, before updating by a member of the Broyden family of updates for quasi-Newton optimization methods. By extensive computational experiments carried out on a set of standard test problems from the CUTE collection, using efficient implementations of the quasi-Newton method, we show that the proposed new scaling factors are better, in terms of efficiency achieved (number of iterations, number of function and gradient evaluations), than the standard choice proposed in the literature.