Local Convergence Properties 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


Abstract. We  consider the local convergence properties
of  the  class  of  augmented  Lagrangian  methods  for
solving nonlinear  programming  problems  whose  global
convergence  properties  are  analyzed by Conn  et  al.
(1993).   In  these  methods,  linear  constraints  are
treated   separately  from  more  general  constraints.
These  latter  constraints   are  combined   with   the
objective function in an augmented Lagrangian while the
subproblem then  consists of (approximately) minimizing
this  augmented  Lagrangian   subject  to  the   linear
constraints.  The stopping rule  that  we  consider for
the inner  iteration covers  practical  tests  used  in
several  existing  packages  for  linearly  constrained
optimization.   Our algorithmic  class  allows  several
distinct  penalty  parameters  to  be  associated  with
different subsets of general equality  constraints.  In
this paper, we  analyze  the local  convergence of  the
sequence of  iterates generated by  this technique  and
prove  fast  linear convergence and boundedness of  the
potentially troublesome penalty parameters.