Armijo-type condition 
                       for the determination 
                   of a Generalized Cauchy Point 
                     in trust region algorithms
                 using exact or inexact projections 
                       on convex constraints
  
                          by A. Sartenaer

                           Report 92/13

Abstract.  This paper considers  some aspects of  two classes of trust
region methods for  solving  constrained  optimization problems.   The
first class proposed by Toint uses techniques based  on the explicitly
calculated projected gradient while the second class proposed by Conn,
Gould, Sartenaer  and Toint  allows  for  inexact projections  on  the
constraints.  We propose and analyze, for each class, a step-size rule
in the   spirit of   the   Armijo rule  for  the  determination  of  a
Generalized Cauchy Point.  We then prove under  mild assumptions that,
in both cases, the classes  preserve  their  theoretical properties of
global convergence and identification of the  correct  active set in a
finite number of  iterations. Numerical issues  are also discussed for
both classes.