# An Overview of the Burer-Monteiro Method for Certifiable Robot Perception

arXiv: https://arxiv.org/abs/2410.00117 · HTML: https://mlsanity.com/paper/2410.00117/

## Key facts

- Cited by 5 papers in the map (data through 14 Oct 2026).
- Builds on 22 of its 44 references that are in the map.
- First posted on arXiv 30 Sep 2024.

## Builds on (most cited first, 22 of 22)

- [Convex optimization](https://mlsanity.com/paper/2106.01946/) (2021)
- [Manopt, a Matlab toolbox for optimization on manifolds](https://mlsanity.com/paper/1308.5200/) (2013)
- [Pymanopt: A Python Toolbox for Optimization on Manifolds using Automatic Differentiation](https://mlsanity.com/paper/1603.03236/) (2016)
- [SE-Sync: A Certifiably Correct Algorithm for Synchronization over the Special Euclidean Group](https://mlsanity.com/paper/1612.07386/) (2016)
- [Shonan Rotation Averaging: Global Optimality by Surfing SO(p)n](https://mlsanity.com/paper/2008.02737/) (2020)
- [One Ring to Rule Them All: Certifiably Robust Geometric Perception with Outliers](https://mlsanity.com/paper/2006.06769/) (2020)
- [Distributed Certifiably Correct Pose-Graph Optimization](https://mlsanity.com/paper/1911.03721/) (2019)
- [A Riemannian low-rank method for optimization over semidefinite matrices with block-diagonal constraints](https://mlsanity.com/paper/1506.00575/) (2015)
- [A Survey of Recent Scalability Improvements for Semidefinite Programming with Applications in Machine Learning, Control, and Robotics](https://mlsanity.com/paper/1908.05209/) (2019)
- [Block Coordinate Descent on Smooth Manifolds: Convergence Theory and Twenty-One Examples](https://mlsanity.com/paper/2305.14744/) (2023)
- [On the local stability of semidefinite relaxations](https://mlsanity.com/paper/1710.04287/) (2017)
- [D2SLAM: Decentralized and Distributed Collaborative Visual-inertial SLAM System for Aerial Swarm](https://mlsanity.com/paper/2211.01538/) (2022)
- [An Efficient Global Optimality Certificate for Landmark-Based SLAM](https://mlsanity.com/paper/2206.12961/) (2022)
- [Certifiably Correct Range-Aided SLAM](https://mlsanity.com/paper/2302.11614/) (2023)
- [Asynchronous and Parallel Distributed Pose Graph Optimization](https://mlsanity.com/paper/2003.03281/) (2020)
- [Majorization Minimization Methods for Distributed Pose Graph Optimization](https://mlsanity.com/paper/2108.00083/) (2021)
- [Certifiably Optimal Rotation and Pose Estimation Based on the Cayley Map](https://mlsanity.com/paper/2308.12418/) (2023)
- [CPL-SLAM: Efficient and Certifiably Correct Planar Graph-Based SLAM Using the Complex Number Representation](https://mlsanity.com/paper/2007.06708/) (2020)
- [Accelerated Inference in Markov Random Fields via Smooth Riemannian Optimization](https://mlsanity.com/paper/1810.11689/) (2018)
- [Toward Globally Optimal State Estimation Using Automatically Tightened Semidefinite Relaxations](https://mlsanity.com/paper/2308.05783/) (2023)
- [Riemannian Optimization for Active Mapping with Robot Teams](https://mlsanity.com/paper/2404.18321/) (2024)
- [Asynchronous Distributed Smoothing and Mapping via On-Manifold Consensus ADMM](https://mlsanity.com/paper/2310.12320/) (2023)

## Built on by (most cited first, 5 of 5)

- [Advances in Global Solvers for 3D Vision](https://mlsanity.com/paper/2602.14662/) (2026)
- [Category-Level Object Shape and Pose Estimation in Less Than a Millisecond](https://mlsanity.com/paper/2509.18979/) (2025)
- [Fast globally optimal Truncated Least Squares point cloud registration with fixed rotation axis](https://mlsanity.com/paper/2508.15613/) (2025)
- [Certifiable Factor Graph Optimization](https://mlsanity.com/paper/2603.01267/) (2026)
- [(DNN)2: Doubly Non-Negative Relaxations for Deep Neural Networks](https://mlsanity.com/paper/2608.24743/) (2026)

## Abstract (arXiv)

This paper presents an overview of the Burer-Monteiro method (BM), a technique that has been applied to solve robot perception problems to certifiable optimality in real-time. BM is often used to solve semidefinite programming relaxations, which can be used to perform global optimization for non-convex perception problems. Specifically, BM leverages the low-rank structure of typical semidefinite programs to dramatically reduce the computational cost of performing optimization. This paper discusses BM in certifiable perception, with three main objectives: (i) to consolidate information from the literature into a unified presentation, (ii) to elucidate the role of the linear independence constraint qualification (LICQ), a concept not yet well-covered in certifiable perception literature, and (iii) to share practical considerations that are discussed among practitioners but not thoroughly covered in the literature. Our general aim is to offer a practical primer for applying BM towards certifiable perception.