Identifying active manifolds

Determining the ‘active manifold’ for a minimization problem is a large step towards solving the problem. Many researchers have studied under what conditions certain algorithms identify active manifolds in a finite number of iterations. In this work we outline a unifying framework encompassing many earlier results on identification via the Subgradient (Gradient) Projection Method, Newton-like Methods, and the Proximal Point Algorithm. This framework, prox-regular partial smoothness, has the advantage of not requiring convexity for its conclusions, and therefore extends many of these earlier results.