We develop a new active-set method for nonlinear programming problems that solves a regularized linear program to predict the active set and then fixes the active constraints to solve an equality-constrained quadratic program for fast convergence. Global convergence is promoted through the use of a filter. We show that the regularization parameter fulfills the same role as a trust-region parameter, and we give global convergence results. In addition, we show that the method identifies the optimal active set once it is sufficiently close to a regular solution. We also comment on alternative regularized problems that allow the inclusion of curvature information into the active-set identification.
Preprint ANL/MCS-P1456-0907, Argonne, IL, September 10, 2007