Convergence properties of minimization algorithms 
              for convex constraints
         using a structured trust region

    A.R. Conn, Nick Gould and Ph.L. Toint

                Report 93/11


Abstract.  We present  in  this paper a  class  of
trust region algorithms in  which the structure of
the  problem   is  explicitly  used  in  the  very
definition  of  the  trust  region  itself.   This
development is intended to reflect the possibility
that  some  parts  of  the  problem  may  be  more
``trusted''  than  others,  a  commonly  occurring
situation  in large-scale  nonlinear applications.
After  describing  the   structured  trust  region
mechanism,  we  prove global convergence  for  all
algorithms in our class.  We also prove that, when
convex constraints are present, the correct set of
such constraints active  at the problem's solution
is  identified by  these algorithms after a finite
number of iterations.