A tensor trust-region model for nonlinear system
Abstract It has turned out that the tensor expansion model has better approximation to the objective function than models of the normal second Taylor expansion. This paper conducts a study of the tensor model for nonlinear equations and it includes the following: (i) a three dimensional symmetric te...
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| Format: | Article |
| Language: | English |
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SpringerOpen
2018-12-01
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| Series: | Journal of Inequalities and Applications |
| Subjects: | |
| Online Access: | http://link.springer.com/article/10.1186/s13660-018-1935-0 |
| _version_ | 1819211135713280000 |
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| author | Songhua Wang Shulun Liu |
| author_facet | Songhua Wang Shulun Liu |
| author_sort | Songhua Wang |
| collection | DOAJ |
| description | Abstract It has turned out that the tensor expansion model has better approximation to the objective function than models of the normal second Taylor expansion. This paper conducts a study of the tensor model for nonlinear equations and it includes the following: (i) a three dimensional symmetric tensor trust-region subproblem model of the nonlinear equations is presented; (ii) the three dimensional symmetric tensor is replaced by interpolating function and gradient values from the most recent past iterate, which avoids the storage of the three dimensional symmetric tensor and decreases the workload of the computer; (iii) the limited BFGS quasi-Newton update is used instead of the second Jacobian matrix, which generates an inexpensive computation of a complex system; (iv) the global convergence is proved under suitable conditions. Numerical experiments are done to show that this proposed algorithm is competitive with the normal algorithm. |
| first_indexed | 2024-12-23T06:22:16Z |
| format | Article |
| id | doaj.art-562bbb4a99df4aa68e06a2115aa1987b |
| institution | Directory Open Access Journal |
| issn | 1029-242X |
| language | English |
| last_indexed | 2024-12-23T06:22:16Z |
| publishDate | 2018-12-01 |
| publisher | SpringerOpen |
| record_format | Article |
| series | Journal of Inequalities and Applications |
| spelling | doaj.art-562bbb4a99df4aa68e06a2115aa1987b2022-12-21T17:57:10ZengSpringerOpenJournal of Inequalities and Applications1029-242X2018-12-012018111410.1186/s13660-018-1935-0A tensor trust-region model for nonlinear systemSonghua Wang0Shulun Liu1School of Mathematics and Statistics, Baise UniversityDepartment of Information Engineering, Jiyuan Vocational and Technical CollegeAbstract It has turned out that the tensor expansion model has better approximation to the objective function than models of the normal second Taylor expansion. This paper conducts a study of the tensor model for nonlinear equations and it includes the following: (i) a three dimensional symmetric tensor trust-region subproblem model of the nonlinear equations is presented; (ii) the three dimensional symmetric tensor is replaced by interpolating function and gradient values from the most recent past iterate, which avoids the storage of the three dimensional symmetric tensor and decreases the workload of the computer; (iii) the limited BFGS quasi-Newton update is used instead of the second Jacobian matrix, which generates an inexpensive computation of a complex system; (iv) the global convergence is proved under suitable conditions. Numerical experiments are done to show that this proposed algorithm is competitive with the normal algorithm.http://link.springer.com/article/10.1186/s13660-018-1935-0Tensor modelTrust regionNonlinear equationsBFGS formulaConvergence |
| spellingShingle | Songhua Wang Shulun Liu A tensor trust-region model for nonlinear system Journal of Inequalities and Applications Tensor model Trust region Nonlinear equations BFGS formula Convergence |
| title | A tensor trust-region model for nonlinear system |
| title_full | A tensor trust-region model for nonlinear system |
| title_fullStr | A tensor trust-region model for nonlinear system |
| title_full_unstemmed | A tensor trust-region model for nonlinear system |
| title_short | A tensor trust-region model for nonlinear system |
| title_sort | tensor trust region model for nonlinear system |
| topic | Tensor model Trust region Nonlinear equations BFGS formula Convergence |
| url | http://link.springer.com/article/10.1186/s13660-018-1935-0 |
| work_keys_str_mv | AT songhuawang atensortrustregionmodelfornonlinearsystem AT shulunliu atensortrustregionmodelfornonlinearsystem AT songhuawang tensortrustregionmodelfornonlinearsystem AT shulunliu tensortrustregionmodelfornonlinearsystem |