A Hybrid Second-Order Method for Homogenous Polynomial Optimization over Unit Sphere
© 2017, Operations Research Society of China, Periodicals Agency of Shanghai University, Science Press, and Springer-Verlag Berlin Heidelberg.In this paper, we propose a hybrid second-order method for homogenous polynomial optimization over the unit sphere in which the new iterate is generated by em...
| Main Authors: | , |
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| Format: | Journal Article |
| Published: |
Springer
2017
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| Online Access: | http://hdl.handle.net/20.500.11937/52420 |
| _version_ | 1848758922184228864 |
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| author | Wang, Y. Zhou, Guanglu |
| author_facet | Wang, Y. Zhou, Guanglu |
| author_sort | Wang, Y. |
| building | Curtin Institutional Repository |
| collection | Online Access |
| description | © 2017, Operations Research Society of China, Periodicals Agency of Shanghai University, Science Press, and Springer-Verlag Berlin Heidelberg.In this paper, we propose a hybrid second-order method for homogenous polynomial optimization over the unit sphere in which the new iterate is generated by employing the second-order information of the objective function. To guarantee the convergence, we recall the shifted power method when the second-order method does not make an improvement to the objective function. As the Hessian of the objective function can easily be computed and no line search is involved in the second-order iterative step, the method is not time-consuming. Further, the new iterate is generated in a relatively larger region and thus the global maximum can be likely obtained. The given numerical experiments show the efficiency of the proposed method. |
| first_indexed | 2025-11-14T09:51:41Z |
| format | Journal Article |
| id | curtin-20.500.11937-52420 |
| institution | Curtin University Malaysia |
| institution_category | Local University |
| last_indexed | 2025-11-14T09:51:41Z |
| publishDate | 2017 |
| publisher | Springer |
| recordtype | eprints |
| repository_type | Digital Repository |
| spelling | curtin-20.500.11937-524202017-09-13T15:39:22Z A Hybrid Second-Order Method for Homogenous Polynomial Optimization over Unit Sphere Wang, Y. Zhou, Guanglu © 2017, Operations Research Society of China, Periodicals Agency of Shanghai University, Science Press, and Springer-Verlag Berlin Heidelberg.In this paper, we propose a hybrid second-order method for homogenous polynomial optimization over the unit sphere in which the new iterate is generated by employing the second-order information of the objective function. To guarantee the convergence, we recall the shifted power method when the second-order method does not make an improvement to the objective function. As the Hessian of the objective function can easily be computed and no line search is involved in the second-order iterative step, the method is not time-consuming. Further, the new iterate is generated in a relatively larger region and thus the global maximum can be likely obtained. The given numerical experiments show the efficiency of the proposed method. 2017 Journal Article http://hdl.handle.net/20.500.11937/52420 10.1007/s40305-016-0148-9 Springer restricted |
| spellingShingle | Wang, Y. Zhou, Guanglu A Hybrid Second-Order Method for Homogenous Polynomial Optimization over Unit Sphere |
| title | A Hybrid Second-Order Method for Homogenous Polynomial Optimization over Unit Sphere |
| title_full | A Hybrid Second-Order Method for Homogenous Polynomial Optimization over Unit Sphere |
| title_fullStr | A Hybrid Second-Order Method for Homogenous Polynomial Optimization over Unit Sphere |
| title_full_unstemmed | A Hybrid Second-Order Method for Homogenous Polynomial Optimization over Unit Sphere |
| title_short | A Hybrid Second-Order Method for Homogenous Polynomial Optimization over Unit Sphere |
| title_sort | hybrid second-order method for homogenous polynomial optimization over unit sphere |
| url | http://hdl.handle.net/20.500.11937/52420 |