Determination of optimal parameters for trust region methods in nonlinear optimization

Trust region techniques are known to be robust and competitive methods
for large-scale nonlinear optimization. Their efficiency depends in
particular on a good choice for the updating rules of the trust-region
radius in the course of the solution. Our purpose is to
investigate the determination of optimal parameters regarding both the
update of the trust region and the acceptance of the trial step. With
this in mind, we have implemented a code that allows such a determination
of optimal parameters by covering a very large sample of potential
values, each of which is being tested on a large set of problems from the
CUTE collection. Using statistical tools, we draw general conclusions
from the extensive set of results to determine optimal values for the parameters.