Exploitation of negative cuvature in algorithms for unconstrained optimization

Today's algoritms for unconstrained optimization
use directions of negative curvature when they
can be found (exact trust regions, truncated
conjugate gradients or curvilinear searches), but
this use is often made difficult because the
scaling of these directions is usually difficult
to estimate. We investigate a technique that
allows the choice between a positive and a
negative curvature designed to minimize the impact
of scaling. Numerical tests show the practical
potential of this technique.