On the triality theory for a quartic polynomial optimization problem
This paper presents a detailed proof of the triality theorem for a class of fourth-order polynomial optimization problems. The method is based on linear algebra but it solves an open problem on the double-min duality. Results show that the triality theory holds strongly in the tri-duality form for o...
| Main Authors: | , |
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| Format: | Journal Article |
| Published: |
2012
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| Online Access: | http://hdl.handle.net/20.500.11937/39610 |
| _version_ | 1848755637833433088 |
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| author | Gao, D. Wu, Changzhi |
| author_facet | Gao, D. Wu, Changzhi |
| author_sort | Gao, D. |
| building | Curtin Institutional Repository |
| collection | Online Access |
| description | This paper presents a detailed proof of the triality theorem for a class of fourth-order polynomial optimization problems. The method is based on linear algebra but it solves an open problem on the double-min duality. Results show that the triality theory holds strongly in the tri-duality form for our problem if the primal problem and its canonical dual have the same dimension; otherwise, both the canonical min-max duality and the double-max duality still hold strongly, but the double-min duality holds weakly in a symmetrical form. Some numerical examples are presented to illustrate that this theory can be used to identify not only the global minimum, but also the local minimum and local maximum. |
| first_indexed | 2025-11-14T08:59:29Z |
| format | Journal Article |
| id | curtin-20.500.11937-39610 |
| institution | Curtin University Malaysia |
| institution_category | Local University |
| last_indexed | 2025-11-14T08:59:29Z |
| publishDate | 2012 |
| recordtype | eprints |
| repository_type | Digital Repository |
| spelling | curtin-20.500.11937-396102017-09-13T15:05:24Z On the triality theory for a quartic polynomial optimization problem Gao, D. Wu, Changzhi This paper presents a detailed proof of the triality theorem for a class of fourth-order polynomial optimization problems. The method is based on linear algebra but it solves an open problem on the double-min duality. Results show that the triality theory holds strongly in the tri-duality form for our problem if the primal problem and its canonical dual have the same dimension; otherwise, both the canonical min-max duality and the double-max duality still hold strongly, but the double-min duality holds weakly in a symmetrical form. Some numerical examples are presented to illustrate that this theory can be used to identify not only the global minimum, but also the local minimum and local maximum. 2012 Journal Article http://hdl.handle.net/20.500.11937/39610 10.3934/jimo.2012.8.229 unknown |
| spellingShingle | Gao, D. Wu, Changzhi On the triality theory for a quartic polynomial optimization problem |
| title | On the triality theory for a quartic polynomial optimization problem |
| title_full | On the triality theory for a quartic polynomial optimization problem |
| title_fullStr | On the triality theory for a quartic polynomial optimization problem |
| title_full_unstemmed | On the triality theory for a quartic polynomial optimization problem |
| title_short | On the triality theory for a quartic polynomial optimization problem |
| title_sort | on the triality theory for a quartic polynomial optimization problem |
| url | http://hdl.handle.net/20.500.11937/39610 |