An Overview of the Burer-Monteiro Method for Certifiable Robot Perception
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| Main Authors: | , , , , |
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| Format: | Preprint |
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2024
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| _version_ | 1866909641976315904 |
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| author | Papalia, Alan Tian, Yulun Rosen, David M. How, Jonathan P. Leonard, John J. |
| author_facet | Papalia, Alan Tian, Yulun Rosen, David M. How, Jonathan P. Leonard, John J. |
| contents | 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. |
| format | Preprint |
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arxiv_https___arxiv_org_abs_2410_00117 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | An Overview of the Burer-Monteiro Method for Certifiable Robot Perception Papalia, Alan Tian, Yulun Rosen, David M. How, Jonathan P. Leonard, John J. Robotics Computer Vision and Pattern Recognition Machine Learning 49, 68 I.4.0; I.5.0; J.2 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. |
| title | An Overview of the Burer-Monteiro Method for Certifiable Robot Perception |
| topic | Robotics Computer Vision and Pattern Recognition Machine Learning 49, 68 I.4.0; I.5.0; J.2 |
| url | https://arxiv.org/abs/2410.00117 |