Sensitivity of trust-region algorithms on their parameters

              N. Gould, D. Orban, A. Sartenaer Ph. L. Toint

                   Report 04/07  August 10th, 2004

In this paper, we examine the sensitivity of trust-region algorithms on the
parameters related to the step acceptance and update of the trust region. 
We show, in the context of unconstrained programming, that the numerical
efficiency of these algorithms can easily be improved by choosing appropriate
parameters.  Recommanded ranges of values for these parameters are exhibited
on the basis of extensive numerical tests.

Keywords: unconstrained programming, trust-region methods, 
          algorithmic parameters.