Vol 2 No 2 (2007)

Identifying Active Manifolds

Warren L. Hare
IRMACS, Simon Fraser University
Adrian S. Lewis
Published September 2, 2007
  • Nonsmooth Optimization,
  • Nonconvex Optimization,
  • Active Constraint Identification,
  • Prox-regular,
  • Partly Smooth
How to Cite
Hare, W. L., & Lewis, A. S. (2007). Identifying Active Manifolds. Algorithmic Operations Research, 2(2), 75. Retrieved from https://journals.lib.unb.ca/index.php/AOR/article/view/2793


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.