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.