Nonnegative polynomial optimization over unit spheres and convex programming relaxations
We consider approximation algorithms for nonnegative polynomial optimization over unit spheres. Such optimization models have wide applications, e.g., in signal and image processing, high order statistics, and computer vision. Since polynomial functions are nonconvex, the problems under consideratio...
| Main Authors: | , , , |
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| Format: | Journal Article |
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Society for Industrial and Applied Mathematics
2012
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| Subjects: | |
| Online Access: | http://hdl.handle.net/20.500.11937/46637 |
| _version_ | 1848757615121661952 |
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| author | Zhou, Guanglu Caccetta, Louis Teo, Kok Lay Wu, S. |
| author_facet | Zhou, Guanglu Caccetta, Louis Teo, Kok Lay Wu, S. |
| author_sort | Zhou, Guanglu |
| building | Curtin Institutional Repository |
| collection | Online Access |
| description | We consider approximation algorithms for nonnegative polynomial optimization over unit spheres. Such optimization models have wide applications, e.g., in signal and image processing, high order statistics, and computer vision. Since polynomial functions are nonconvex, the problems under consideration are all NP-hard. In this paper, based on convex polynomial optimization relaxations, we propose polynomial-time approximation algorithms with new approximation bounds. Numerical results are reported to show the effectiveness of the proposed approximation algorithms. |
| first_indexed | 2025-11-14T09:30:54Z |
| format | Journal Article |
| id | curtin-20.500.11937-46637 |
| institution | Curtin University Malaysia |
| institution_category | Local University |
| last_indexed | 2025-11-14T09:30:54Z |
| publishDate | 2012 |
| publisher | Society for Industrial and Applied Mathematics |
| recordtype | eprints |
| repository_type | Digital Repository |
| spelling | curtin-20.500.11937-466372017-09-13T14:08:02Z Nonnegative polynomial optimization over unit spheres and convex programming relaxations Zhou, Guanglu Caccetta, Louis Teo, Kok Lay Wu, S. nonnegative polynomial optimization approximation - algorithm convex optimization relaxation We consider approximation algorithms for nonnegative polynomial optimization over unit spheres. Such optimization models have wide applications, e.g., in signal and image processing, high order statistics, and computer vision. Since polynomial functions are nonconvex, the problems under consideration are all NP-hard. In this paper, based on convex polynomial optimization relaxations, we propose polynomial-time approximation algorithms with new approximation bounds. Numerical results are reported to show the effectiveness of the proposed approximation algorithms. 2012 Journal Article http://hdl.handle.net/20.500.11937/46637 10.1137/110827910 Society for Industrial and Applied Mathematics fulltext |
| spellingShingle | nonnegative polynomial optimization approximation - algorithm convex optimization relaxation Zhou, Guanglu Caccetta, Louis Teo, Kok Lay Wu, S. Nonnegative polynomial optimization over unit spheres and convex programming relaxations |
| title | Nonnegative polynomial optimization over unit spheres and convex programming relaxations |
| title_full | Nonnegative polynomial optimization over unit spheres and convex programming relaxations |
| title_fullStr | Nonnegative polynomial optimization over unit spheres and convex programming relaxations |
| title_full_unstemmed | Nonnegative polynomial optimization over unit spheres and convex programming relaxations |
| title_short | Nonnegative polynomial optimization over unit spheres and convex programming relaxations |
| title_sort | nonnegative polynomial optimization over unit spheres and convex programming relaxations |
| topic | nonnegative polynomial optimization approximation - algorithm convex optimization relaxation |
| url | http://hdl.handle.net/20.500.11937/46637 |