Automatic Decrease 
                     of the Penalty Parameter
                 in Exact Penalty Function Methods

                   by M. Mongeau and A. Sartenaer

                            Report 93/02      

Abstract.  This  paper presents an analysis of  the involvement of the
penalty parameter   in  exact penalty function  methods    that yields
modifications to the standard outer loop  which  decreases the penalty
parameter   (typically dividing  it by  a   constant).  The  procedure
presented  is based on  the  simple  idea    of  making explicit   the
dependence of the penalty function  upon  the penalty parameter and is
illustrated on  a  linear  programming problem with   the  $l_1$ exact
penalty function and an active-set approach.   The procedure decreases
the  penalty  parameter,  when needed,  to  the {\em  maximal\/} value
allowing  the  inner   minimization  algorithm  to leave   the current
iterate.  It moreover avoids unnecessary calculations in the iteration
following the step in  which the  penalty parameter is  decreased.  We
report  on  preliminary  computational  results which  show  that this
method  can require fewer iterations than  the  standard way to update
the penalty parameter.   This approach permits  a better understanding
of the performance of exact penalty methods.