A family of minimum curvature variable-methods for unconstrained optimization. (c1998)

Abstract

The major objective of the work in this thesis concentrates on deriving a Variable-Metric family of minimum curvature multi-step quasi-Newton methods for unconstrained optimization. The aim is to provide further gains in numerical performance to those obtained by the multi-step methods developed earlier, as well as to develop a general framework that encompasses all possible multi-step minimum curvature algorithms generated by appropriate parameter choices. The derivation will be based on a selected rational model with a free parameter, oriented towards securing a "smooth" interpolation of the points defining the multi-step curve. Different choices of the metric used in parameterizing the curves needed for updating the inverse Hessian approximation at each iteration, are tested and numerical results are then reported.