A recursive trust-region method in infinity norm
             for bound-constrained nonlinear optimization

Serge Gratton  Melodie Mouffe  Philippe L. Toint  Melissa Weber-Mendonca

             Report 07/01                      23 APril 2007


A recursive trust-region method is introduced for the solution of
bound-constrained nonlinear nonconvex optimization problems for which a
hierarchy of descriptions exists. Typical cases are infinite-dimensional
problems for which the levels of the hierarchy correspond to discretization
levels, from coarse to fine.  The new method uses the infinity norm to define
the shape of the trust region, which is well adapted to the handling of bounds
and also to the use of successive coordinate minimization as a smoothing
technique. Some numerical tests are presented to motivate a theoretical
analysis showing convergence to first-order critical points irrespective of
the given starting point.