On the Identification of Active Constraints
James V. Burke, Jorge J. Morè · SIAM Journal on Numerical Analysis · 1988
Nondegeneracy conditions that guarantee that the optimal active constraints are identified in a finite number of iterations are studied. Results of this type have only been established for a few algorithms, and then under restrictive hypothesis. The main result is a characterization of those algorithms that identify the optimal constraints in a finite number of iterations. This result is obtained with a nondegeneracy assumption which is equivalent, in the standard nonlinear programming problem, to the assumption that there is a set of strictly complementary Lagrange multipliers. As an important consequence of the authors’ results the way that this characterization applies to gradient projection and sequential quadratic programming algorithms is shown.