Nonmonotone spectral gradient method based on memoryless symmetric rank-one update for large-scale unconstrained optimization
This paper proposes a nonmonotone spectral gradient method for solving large-scale unconstrained optimization problems. The spectral parameter is derived from the eigenvalues of an optimally sized memoryless symmetric rank-one matrix obtained under the measure defined as a ratio of the determinant...
| Main Authors: | , , , |
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| Format: | Article |
| Published: |
American Institute of Mathematical Sciences
2021
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| Online Access: | http://psasir.upm.edu.my/id/eprint/94373/ |
| _version_ | 1848861979390771200 |
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| author | Hong, Seng Sim Chuei, Yee Chen Wah, June Leong Jiao, Li |
| author_facet | Hong, Seng Sim Chuei, Yee Chen Wah, June Leong Jiao, Li |
| author_sort | Hong, Seng Sim |
| building | UPM Institutional Repository |
| collection | Online Access |
| description | This paper proposes a nonmonotone spectral gradient method for
solving large-scale unconstrained optimization problems. The spectral parameter is derived from the eigenvalues of an optimally sized memoryless symmetric
rank-one matrix obtained under the measure defined as a ratio of the determinant of updating matrix over its largest eigenvalue. Coupled with a nonmonotone line search strategy where backtracking-type line search is applied
selectively, the spectral parameter acts as a stepsize during iterations when no
line search is performed and as a milder form of quasi-Newton update when
backtracking line search is employed. Convergence properties of the proposed
method are established for uniformly convex functions. Extensive numerical
experiments are conducted and the results indicate that our proposed spectral
gradient method outperforms some standard conjugate-gradient methods. |
| first_indexed | 2025-11-15T13:09:44Z |
| format | Article |
| id | upm-94373 |
| institution | Universiti Putra Malaysia |
| institution_category | Local University |
| last_indexed | 2025-11-15T13:09:44Z |
| publishDate | 2021 |
| publisher | American Institute of Mathematical Sciences |
| recordtype | eprints |
| repository_type | Digital Repository |
| spelling | upm-943732023-04-04T04:25:06Z http://psasir.upm.edu.my/id/eprint/94373/ Nonmonotone spectral gradient method based on memoryless symmetric rank-one update for large-scale unconstrained optimization Hong, Seng Sim Chuei, Yee Chen Wah, June Leong Jiao, Li This paper proposes a nonmonotone spectral gradient method for solving large-scale unconstrained optimization problems. The spectral parameter is derived from the eigenvalues of an optimally sized memoryless symmetric rank-one matrix obtained under the measure defined as a ratio of the determinant of updating matrix over its largest eigenvalue. Coupled with a nonmonotone line search strategy where backtracking-type line search is applied selectively, the spectral parameter acts as a stepsize during iterations when no line search is performed and as a milder form of quasi-Newton update when backtracking line search is employed. Convergence properties of the proposed method are established for uniformly convex functions. Extensive numerical experiments are conducted and the results indicate that our proposed spectral gradient method outperforms some standard conjugate-gradient methods. American Institute of Mathematical Sciences 2021-09 Article PeerReviewed Hong, Seng Sim and Chuei, Yee Chen and Wah, June Leong and Jiao, Li (2021) Nonmonotone spectral gradient method based on memoryless symmetric rank-one update for large-scale unconstrained optimization. Journal of Industrial and Management Optimization, 18 (6). pp. 3975-3988. ISSN 1547-5816; ESSN: 1553-166X https://www.aimsciences.org/article/doi/10.3934/jimo.2021143 10.3934/jimo.2021143 |
| spellingShingle | Hong, Seng Sim Chuei, Yee Chen Wah, June Leong Jiao, Li Nonmonotone spectral gradient method based on memoryless symmetric rank-one update for large-scale unconstrained optimization |
| title | Nonmonotone spectral gradient method based on memoryless symmetric rank-one update for large-scale unconstrained optimization |
| title_full | Nonmonotone spectral gradient method based on memoryless symmetric rank-one update for large-scale unconstrained optimization |
| title_fullStr | Nonmonotone spectral gradient method based on memoryless symmetric rank-one update for large-scale unconstrained optimization |
| title_full_unstemmed | Nonmonotone spectral gradient method based on memoryless symmetric rank-one update for large-scale unconstrained optimization |
| title_short | Nonmonotone spectral gradient method based on memoryless symmetric rank-one update for large-scale unconstrained optimization |
| title_sort | nonmonotone spectral gradient method based on memoryless symmetric rank-one update for large-scale unconstrained optimization |
| url | http://psasir.upm.edu.my/id/eprint/94373/ http://psasir.upm.edu.my/id/eprint/94373/ http://psasir.upm.edu.my/id/eprint/94373/ |