A three-term Polak-Ribière-Polyak conjugate gradient method for vector optimization
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arXiv
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| Autori principali: | , |
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| Natura: | Preprint |
| Pubblicazione: |
2025
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| _version_ | 1866915537653596160 |
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| author | Lin, Guangxuan Du, Shouqiang |
| author_facet | Lin, Guangxuan Du, Shouqiang |
| contents | A novel three-term Polak-Ribière-Polyak conjugate gradient method is proposed for solving vector optimization problems. It should be emphasized that this is the first extension of three-term conjugate gradient methods from scalar optimization to vector optimization. The method can consistently generate a sufficient descent direction independent of line search procedures and without modifying the conjugate parameters. This result improves upon the corresponding conclusions in SIAM J. Optim. 28, 2690-2720 (2018), J. Optim. Theory Appl. 204,13 (2025) and Optim. Methods Softw. 28, 725-754 (2025). Based on a new Wolfe-type line search, the global convergence of the proposed scheme is established without imposing restrictions such as self-adjusting strategies, regular restarts and convexity assumptions. Numerical experiments demonstrate the favourable performance of the proposed method. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2505_08408 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | A three-term Polak-Ribière-Polyak conjugate gradient method for vector optimization Lin, Guangxuan Du, Shouqiang Optimization and Control 90C29, 90C52 A novel three-term Polak-Ribière-Polyak conjugate gradient method is proposed for solving vector optimization problems. It should be emphasized that this is the first extension of three-term conjugate gradient methods from scalar optimization to vector optimization. The method can consistently generate a sufficient descent direction independent of line search procedures and without modifying the conjugate parameters. This result improves upon the corresponding conclusions in SIAM J. Optim. 28, 2690-2720 (2018), J. Optim. Theory Appl. 204,13 (2025) and Optim. Methods Softw. 28, 725-754 (2025). Based on a new Wolfe-type line search, the global convergence of the proposed scheme is established without imposing restrictions such as self-adjusting strategies, regular restarts and convexity assumptions. Numerical experiments demonstrate the favourable performance of the proposed method. |
| title | A three-term Polak-Ribière-Polyak conjugate gradient method for vector optimization |
| topic | Optimization and Control 90C29, 90C52 |
| url | https://arxiv.org/abs/2505.08408 |