Line-Search and Trust-Region Equations for a Primal-Dual Interior Method for Nonlinear Optimization
by Philip E. Gill, Daniel P. Robinson, Vyacheslav Kungurtsev
The approximate Newton equations for a minimizing a shifted primal-dual penalty-barrier method are derived for a nonlinearly constrained problem in general form. These equations may be used in conjunction with either a line-search or trust-region method to force convergence from an arbitrary starting point. It is shown that under certain conditions, the approximate Newton equations are equivalent to a regularized form of the conventional primal-dual path-following equations.