# On computing Goldstein approximate second-order stationary points of structured nonsmooth nonconvex programs

arXiv: https://arxiv.org/abs/2607.24122 · HTML: https://mlsanity.com/paper/2607.24122/

## Key facts

- Cited by 1 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 27 Jul 2026.

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

- [The Exponential Price of Determinism in Nonsmooth Nonconvex Optimization](https://mlsanity.com/paper/2609.23837/) (2026)

## Abstract (arXiv)

In this paper, we exhibit a randomized first-order algorithm to compute Goldstein approximate second-order stationary points of L-smooth functions, using tools from randomized smoothing. The algorithm has oracle complexity widetildeO( n2/varepsilon9+ n3/varepsilon7), where n=1,2,ldots is the input dimension and varepsilon>0 is the (common) tolerance. We also present extensions to weakly convex functions and applications to bilevel optimization.