Convergence  Properties  of  an Augmented  Lagrangian
Algorithm  for  Optimization  with a  Combination  of
General Equality and Linear Constraints

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

We  consider   the   global  and  local   convergence
properties of a class of augmented Lagrangian methods
for solving nonlinear programming problems.  In these
methods,  linear  and more  general  constraints  are
handled in  different  ways.  The general constraints
are  combined  with  the  objective  function  in  an
augmented   Lagrangian.  The  iteration  consists  of
solving a sequence of subproblems; in each subproblem
the augmented  Lagrangian  is approximately minimized
in the region  defined by the linear constraints.   A
subproblem  is  terminated  as  soon  as  a  stopping
condition is satisfied.  The stopping  rules that  we
consider  here  encompass  practical  tests  used  in
several  existing packages  for  linearly constrained
optimization.   Our  algorithm  also allows different
penalty  parameters to  be associated  with  disjoint
subsets of the  general constraints.  In this  paper,
we  analyze  the  convergence   of  the  sequence  of
iterates  generated by  such  an algorithm  and prove
global and fast linear convergence as well as showing
that   potentially  troublesome   penalty  parameters
remain bounded away from zero.