active manifolds – 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

Active strict saddles in nonsmooth optimization

Published: 2019/12/15

Nonsmooth Optimization active manifolds, kurdyka-lojasiewicz inequality, proximal algorithms, strict saddles

We introduce a geometrically transparent strict saddle property for nonsmooth functions. This property guarantees that simple proximal algorithms on weakly convex problems converge only to local minimizers, when randomly initialized. We argue that the strict saddle property may be a realistic assumption in applications, since it provably holds for generic semi-algebraic optimization problems. ArticleDownload View … Read more