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Low-rank matrix recovery with Ky Fan 2-k-norm
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Doan, Xuan Vinh and Vavasis, Stephen (2022) Low-rank matrix recovery with Ky Fan 2-k-norm. Journal of Global Optimization, 82 . pp. 727-751. doi:10.1007/s10898-021-01031-0 ISSN 0925-5001.
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Official URL: https://doi.org/10.1007/s10898-021-01031-0
Abstract
Low-rank matrix recovery problem is difficult due to its non-convex properties and it is usually solved using convex relaxation approaches. In this paper, we formulate the non-convex low-rank matrix recovery problem exactly using novel Ky Fan 2-k-norm-based models. A general difference of convex functions algorithm (DCA) is developed to solve these models. A proximal point algorithm (PPA) framework is proposed to solve sub-problems within the DCA, which allows us to handle large instances. Numerical results show that the proposed models achieve high recoverability rates as compared to the truncated nuclear norm method and the alternating bilinear optimization approach. The results also demonstrate that the proposed DCA with the PPA framework is efficient in handling larger instances.
| Item Type: | Journal Article | ||||||||
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| Subjects: | Q Science > QA Mathematics | ||||||||
| Divisions: | Faculty of Social Sciences > Warwick Business School | ||||||||
| Library of Congress Subject Headings (LCSH): | Mathematical optimization, Matrices, Operator theory | ||||||||
| Journal or Publication Title: | Journal of Global Optimization | ||||||||
| Publisher: | Springer | ||||||||
| ISSN: | 0925-5001 | ||||||||
| Official Date: | April 2022 | ||||||||
| Dates: |
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| Volume: | 82 | ||||||||
| Page Range: | pp. 727-751 | ||||||||
| DOI: | 10.1007/s10898-021-01031-0 | ||||||||
| Status: | Peer Reviewed | ||||||||
| Publication Status: | Published | ||||||||
| Access rights to Published version: | Open Access (Creative Commons) | ||||||||
| Date of first compliant deposit: | 29 April 2021 | ||||||||
| Date of first compliant Open Access: | 2 June 2021 | ||||||||
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