Global Convergence of two Augmented Lagrangian 
    Algorithms for Optimization with a Combination 
     of General Equality and Linear Constraints

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

                   Report 93/1

Abstract.  We consider the global convergence  properties
of a class  of  augmented Lagrangian methods for  solving
nonlinear programming  problems.  In the proposed method,
linear  constraints  are  treated  separately  from  more
general constraints.  Thus only the  latter are  combined
with the  objective function in  an augmented Lagrangian.
The   subproblem   then   consists   of   (approximately)
minimizing  this  augmented  Lagrangian  subject  to  the
linear constraints.  In this  paper, we prove the  global
convergence of the sequence of iterates generated by this
technique  to  a  first-order  stationary  point  of  the
original problem.  We consider various stopping rules for
the  iterative  solution  of  the  subproblem,  including
practical  tests used  in  several  existing packages for
linearly  constrained optimization.   We  also extend our
results  to  the  case  where the  augmented Lagrangian's
definition involves several distinct penalty parameters.