Identifying Active Constraints via Partial Smoothness and Prox-Regularity

Active set algorithms, such as the projected gradient method in nonlinear optimization, are designed to "identify" the active constraints of the problem in a finite number of iterations. Using the notions of "partial smoothness" and "prox-regularity" we extend work of Burke, More and Wright on identifiable surfaces from the convex case to a general nonsmooth setting. We further show how this setting can be used in the study of sufficient conditions for local minimizers.