LINE SEARCH PROCEDURES FOR THE LOGARITHMIC BARRIER FUNCTION

Barrier methods for constrained optimization, widely applied in the 19 60s and 1970s, have recently enjoyed a revival of popularity. A line s earch with respect to a logarithmic barrier function or related potent ial function is often part of modern interior methods. Standard line s earch procedures tend to be inefficient in this context for two reason s: an inappropriate choice of initial trial step if any constraints ar e nonlinear, and poor approximation of the barrier function by low-ord er polynomial interpolants. This paper discusses line search strategie s specifically designed for the logarithmic barrier function.