# On second-order weak sharp minima of general nonconvex set-constrained optimization problems

arXiv: https://arxiv.org/abs/2507.12682 · HTML: https://mlsanity.com/paper/2507.12682/

## Key facts

- Cited by 1 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 16 Jul 2025.

## Built on by (most cited first, 1 of 1)

- [Convergence of Spectral Descent for Non-smooth Optimization](https://mlsanity.com/paper/2605.26977/) (2026)

## Abstract (arXiv)

This paper explores local second-order weak sharp minima for a broad class of nonconvex optimization problems. We propose novel second-order optimality conditions formulated through the use of classical and lower generalized support functions. These results are based on asymptotic second-order tangent cones and outer second-order tangent sets. Specifically, our findings eliminate the necessity of assuming convexity in the constraint set and/or the outer second-order tangent set, or the nonemptiness of the outer second-order tangent set. Furthermore, unlike traditional approaches, our sufficient conditions do not rely on strong assumptions such as the uniform second-order regularity of the constraint set and the property of uniform approximation of the critical cones.