ON THE IDENTIFICATION OF ACTIVE CONSTRAINTS .2. THE NONCONVEX CASE

Results on the identification of active constraints are extended to the nonconvex constrained nonlinear programming problem. The approach is motivated by the geometric structure of a certain polyhedral convex 'linearization' of the constraint region at each iteration. Questions of constraint identification are couched in terms of the faces of these polyhedra. The main result employs a nondegeneracy condition and the linear independence condition to obtain a characterization of those algorithms that identify the optimal active constraints in a finite number of iterations. The role of the linear independence condition is carefully examined, and it is argued that it is required within the context of a first-order theory of constraint identification. In conclusion, the characterization theorem is applied to the Wilson-Han-Powell sequential quadratic programming algorithm and Fletecher's QL algorithm.