Geometrically robust least squares through manifold optimization
Fuente:
arXiv
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| Hauptverfasser: | , , |
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| Format: | Preprint |
| Veröffentlicht: |
2025
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| _version_ | 1866909888090734592 |
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| author | Coulson, Jeremy Padoan, Alberto Mostajeran, Cyrus |
| author_facet | Coulson, Jeremy Padoan, Alberto Mostajeran, Cyrus |
| contents | This paper presents a methodology for solving a geometrically robust least squares problem, which arises in various applications where the model is subject to geometric constraints. The problem is formulated as a minimax optimization problem on a product manifold, where one variable is constrained to a ball describing uncertainty. To handle the constraint, an exact penalty method is applied. A first-order gradient descent ascent algorithm is proposed to solve the problem, and its convergence properties are illustrated by an example. The proposed method offers a robust approach to solving a wide range of problems arising in signal processing and data-driven control. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2511_03644 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Geometrically robust least squares through manifold optimization Coulson, Jeremy Padoan, Alberto Mostajeran, Cyrus Optimization and Control Systems and Control This paper presents a methodology for solving a geometrically robust least squares problem, which arises in various applications where the model is subject to geometric constraints. The problem is formulated as a minimax optimization problem on a product manifold, where one variable is constrained to a ball describing uncertainty. To handle the constraint, an exact penalty method is applied. A first-order gradient descent ascent algorithm is proposed to solve the problem, and its convergence properties are illustrated by an example. The proposed method offers a robust approach to solving a wide range of problems arising in signal processing and data-driven control. |
| title | Geometrically robust least squares through manifold optimization |
| topic | Optimization and Control Systems and Control |
| url | https://arxiv.org/abs/2511.03644 |