Global convergence of a class of trust region 
      algorithms for optimization using inexact
        projections on convex constraints

 A.R. Conn, N.I.M. Gould, A. Sartenaer and Ph.L. Toint

                  Report 90/4

Abstract. A class  of trust region  based algorithms is
presented for  the  solution of  nonlinear optimization
problems with a convex feasible set.  At  variance with
previously published analysis of this type, the  theory
presented   allows  for  the  use  of  general   norms.
Furthermore, the proposed algorithms do not require the
explicit computation of the projected gradient, and can
therefore be adapted to cases where the projection onto
the  feasible  domain  may be  expensive  to calculate.
Strong global convergence results  are  derived for the
class.  It is also  shown that  the  set of  linear and
nonlinear constraints that are binding at the  solution
are identified  by  the algorithms  of  the class in  a
finite number of iterations.