A note on using alternative second-order models 
             for the subproblems arising in barrier function 
                      methods for minimization

                                 by

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

                            Report 93/16

              This paper is dedicated to Professor J. Stoer 
                on the occasion of his sixtieth birthday.  

  Abstract. Inequality constrained minimization problems are often solved
  by  considering a  sequence of  parameterized  barrier functions.  Each
  barrier function is approximately minimized and the relevant parameters
  subsequently adjusted.  It is common for  the estimated solution to one
  barrier  function problem to  be used  as  a  starting estimate for the
  next.  However, this has  unfortunate   repercussions for the  standard
  Newton-like methods applied  to the barrier  subproblem.  In this note,
  we   consider a class of  alternative  Newton methods which attempt  to
  avoid such difficulties. Such schemes have already proved of use in the
  Harwell Subroutine Library quadratic programming codes VE14 and VE19.