Abstracts
Abstract
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.
Keywords:
- Nonsmooth Optimization,
- Nonconvex Optimization,
- Active Constraint Identification,
- Prox-regular,
- Partly Smooth
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