Yue Xie – 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

Complexity of a Projected Newton-CG Method for Optimization with Bounds

Published: 2021/03/29, Updated: 2022/06/10

Bound-constrained Optimization Complexity Guarantees, conjugate gradient method, Newton's Method, Nonconvex Bound-constrained Optimization, projected gradient method

This paper describes a method for solving smooth nonconvex minimization problems subject to bound constraints with good worst-case complexity and practical performance. The method contains elements of two existing methods: the classical gradient projection approach for bound-constrained optimization and a recently proposed Newton-conjugate gradient algorithm for unconstrained nonconvex optimization. Using a new definition of approximate … Read more