A NOTE ON USING ALTERNATIVE 2ND-ORDER MODELS FOR THE SUBPROBLEMS ARISING IN BARRIER FUNCTION METHODS FOR MINIMIZATION

Inequality constrained minimization problems are often solved by consi dering a sequence of parameterized barrier functions. Each barrier fun ction is approximately minimized and the relevant parameters subsequen tly adjusted. It is common for the estimated solution to one barrier f unction problem to be used as a starting estimate for the next. Howeve r, this has unfortunate repercussions for the standard Newton-like met hods applied to the barrier subproblem. In this note, we consider a cl ass of alternative Newton methods which attempt to avoid such difficul ties. Such schemes have already proved of use in the Harwell Subroutin e Library quadratic programming codes VE14 and VE19.