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.
