Numerical Experience with a Recursive Trust-Region Method for
                 Multilevel Nonlinear Optimization

              by S. Gratton, A. Sartenaer and Ph. L. Toint

                         Report 06/01  May 2006

We  consider  an  implementation  of  the  recursive  multilevel  trust-region
algorithm  proposed  by  Gratton,  Sartenaer  and Toint  (2004),  and  provide
significant  numerical  experience on  multilevel  test  problems. A  suitable
choice of the algorithm's parameters is identified on these problems, yielding
a  very  satisfactory  compromise  between  reliability  and  efficiency.  The
resulting  default  algorithm is  then  compared  to alternative  optimization
techniques  such as  mesh refinement  and  direct solution  of the  fine-level
problem. The sensibility of the default variant with respect to most important
algorithmic parameters is finally investigated.