An active-set trust-region method for 
         derivative-free nonlinear bound-constrained optimization

              S. Gratton, Ph. L. Toint and A. Troeltzsch

                   Report NAXYS-01-2010 27 August 2010

We  consider   an  implementation   of  a  recursive   model-based  active-set
trust-region  method   for  solving  bound-constrained   nonlinear  non-convex
optimization   problems   without   derivatives   using   the   technique   of
self-correcting geometry proposed in  Scheinberg and Toint (2009). Considering
an active-set  method in model-based  optimization creates the  opportunity of
saving a  substantial amount of function evaluations  when maintaining smaller
interpolation  sets   while  proceeding  optimization   in  lower  dimensional
subspaces. The resulting algorithm is shown to be numerically competitive.