# A Riemannian Dimension-reduced Second Order Method with Application in Sensor Network Localization

arXiv: https://arxiv.org/abs/2304.10092 · HTML: https://mlsanity.com/paper/2304.10092/

## Key facts

- Cited by 3 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 20 Apr 2023.

## Built on by (most cited first, 3 of 3)

- [Riemannian Optimization for Non-convex Euclidean Distance Geometry with Global Recovery Guarantees](https://mlsanity.com/paper/2410.06376/) (2024)
- [Euclidean Distance Matrix Completion via Asymmetric Projected Gradient Descent](https://mlsanity.com/paper/2504.19530/) (2025)
- [Provable Non-Convex Euclidean Distance Matrix Completion: Geometry, Reconstruction, and Robustness](https://mlsanity.com/paper/2508.00091/) (2025)

## Abstract (arXiv)

In this paper, we propose a cubic-regularized Riemannian optimization method (RDRSOM), which partially exploits the second order information and achieves the iteration complexity of O(1/ε3/2). In order to reduce the per-iteration computational cost, we further propose a practical version of (RDRSOM), which is an extension of the well known Barzilai-Borwein method and achieves the iteration complexity of O(1/ε3/2). We apply our method to solve a nonlinear formulation of the wireless sensor network localization problem whose feasible set is a Riemannian manifold that has not been considered in the literature before. Numerical experiments are conducted to verify the high efficiency of our algorithm compared to state-of-the-art Riemannian optimization methods and other nonlinear solvers.