A Globally Convergent Lagrangian Barrier Algorithm 
 for Optimization with General Inequality Constraints 
             and Simple Bounds

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

                 Report 92/07

We   consider   the  global  and   local   convergence
properties of a class of  Lagrangian  barrier  methods
for solving nonlinear  programming problems.  In  such
methods,  simple  bound  constraints  may  be  treated
separately  from   more   general  constraints.    The
objective   and  general   constraint   functions  are
combined in a Lagrangian barrier function.  A sequence
of such  functions are approximately minimized  within
the domain  defined  by  the  simple  bounds.   Global
convergence of the sequence of generated iterates to a
first-order stationary point  for the original problem
is  established.    Furthermore,  possible   numerical
difficulties associated with  barrier function methods
are  avoided  as  it  is  shown  that   a  potentially
troublesome  penalty  parameter is bounded  away  from
zero.  This paper  is a companion to our previous work
on augmented Lagrangian methods.