A quasi-Newton method using a nonquadratic model

AbstractMost “quasi-Newton” methods in common use for function minimisation use a quadratic model to approximate the underlying objective function at the current estimate of the minimum. In this paper we describe new minimisation algorithms derived by replacing the quadratic model with a polynomial type model involving a free parameter which is determined implicitly by means of information about the objective function. We show how this information may be efficiently utilised in an optimisation method of quasi-Newton type. Numerical tests were carried out to demonstrate the performance of the new algorithms in comparison to the standard BFGS method