identifiable set – Optimization Online

On the Absence of Identifiable Manifolds in Finite-Max Composite Optimization

Published: 2026/08/17

In nonsmooth optimization, identifiable sets describe the local region eventually reached by sequences converging to a prescribed critical point. When such a set is a \(C^2\) manifold on which the objective restricts to a \(C^2\) function, it is called an identifiable manifold. Their appeal lies in what they enable: many first-order methods identify these manifolds … Read more

Orthogonal invariance and identifiability

Published: 2013/04/11

Nonsmooth Optimization duality, eigenvalues, identifiable set, partial smoothness, polyhedra, symmetric matrix

Orthogonally invariant functions of symmetric matrices often inherit properties from their diagonal restrictions: von Neumann’s theorem on matrix norms is an early example. We discuss the example of “identifiability”, a common property of nonsmooth functions associated with the existence of a smooth manifold of approximate critical points. Identifiability (or its synonym, “partial smoothness”) is the … Read more