In the vicinity of a solution of a nonlinear programming problem at which both strict complementarity and linear independence of the active constraints may fail to hold, we describe a technique for distinguishing weakly active from strongly active constraints. We show that this information can be used to modify the sequential quadratic programming algorithm so that it exhibits superlinear convergence to the solution under assumptions weaker than those made in previous analyses.
Preprint P865-1200, Mathematics and Computer Science Division, Argonne National Laboratory, December 2000. (Revised December, 2001.) Published in Mathematical Programming, Series B, 95 (2003), pp. 137--160.