# A Trust Region Method for Finding Second-Order Stationarity in Linearly Constrained Non-Convex Optimization

arXiv: https://arxiv.org/abs/1904.06784 · HTML: https://mlsanity.com/paper/1904.06784/

## Key facts

- Cited by 2 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 14 Apr 2019.

## Built on by (most cited first, 2 of 2)

- [Nonnegative Low-rank Matrix Recovery Can Have Spurious Local Minima](https://mlsanity.com/paper/2505.03717/) (2025)
- [HOUDINI: Escaping from Moderately Constrained Saddles](https://mlsanity.com/paper/2205.13753/) (2022)

## Abstract (arXiv)

Motivated by TRACE algorithm [Curtis et al. 2017], we propose a trust region algorithm for finding second order stationary points of a linearly constrained non-convex optimization problem. We show the convergence of the proposed algorithm to (εg, εH)-second order stationary points in widetildeO(maxεg-3/2, εH-3) iterations. This iteration complexity is achieved for general linearly constrained optimization without cubic regularization of the objective function.