identifiability – Optimization Online

Transferability of Error Bounds and the Kurdyka-Lojasiewicz Property under $C^1$ Partial Smoothness

Published: 2026/09/28

Nonlinear Optimization, Nonsmooth Optimization error bound, identifiability, KL property, partial smoothness, slope

This work studies how a generalized error bound (GEB) property in the ambient Euclidean space transfers to the active manifold under $\mathcal{C}^1$ partial smoothness. The GEB generalizes the standard error bound, which upper bounds the distance to a subset of critical points using first-order stationarity residuals, by allowing the distance to be composed with a … Read more

Optimality, identifiability, and sensitivity

Published: 2012/07/27

Nonsmooth Optimization active set, critical cone, fast track, identifiability, normal cone, optimality conditions, partly smooth, prox-regularity, sensitivity analysis, subgradient

Around a solution of an optimization problem, an “identifiable” subset of the feasible region is one containing all nearby solutions after small perturbations to the problem. A quest for only the most essential ingredients of sensitivity analysis leads us to consider identifiable sets that are “minimal”. This new notion lays a broad and intuitive variational-analytic … Read more