On the identification of active constraints
SIAM Journal on Numerical Analysis
Identifiable surfaces in constrained optimization
SIAM Journal on Control and Optimization
On $\mathcalVU$-theory for Functions with Primal-Dual Gradient Structure
SIAM Journal on Optimization
Active Sets, Nonsmoothness, and Sensitivity
SIAM Journal on Optimization
On a Class of Nonsmooth Composite Functions
Mathematics of Operations Research
A **-algorithm for convex minimization
Mathematical Programming: Series A and B
A proximal method for identifying active manifolds
Computational Optimization and Applications
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The past decade has seen the introduction of a number of classes of nonsmooth functions possessing smooth substructure, e.g., "amenable functions", "partly smooth functions", and "g 驴 F decomposable functions". Along with these classes a number of structural properties have been proposed, e.g., "identifiable surfaces", "fast tracks", and "primal-dual gradient structures". In this paper we examine the relationships between these various classes of functions and their smooth substructures.In the convex case we show that the definitions of identifiable surfaces, fast tracks, and partly smooth functions are equivalent. In the nonconvex case we discuss when a primal-dual gradient structure or g 驴 F decomposition implies the function is partly smooth, and vice versa. We further provide examples to show these classes are not equal.