Anderson acceleration of derivative-free projection methods for constrained monotone nonlinear equations
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arXiv
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| Auteurs principaux: | , , |
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| Format: | Preprint |
| Publié: |
2024
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| _version_ | 1866912838873776128 |
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| author | Jin, Jiachen Wang, Hongxia Deng, Kangkang |
| author_facet | Jin, Jiachen Wang, Hongxia Deng, Kangkang |
| contents | The derivative-free projection method (DFPM) is an efficient algorithm for solving monotone nonlinear equations. As problems grow larger, there is a strong demand for speeding up the convergence of DFPM. This paper considers the application of Anderson acceleration (AA) to DFPM for constrained monotone nonlinear equations. By employing a nonstationary relaxation parameter and interleaving with slight modifications in each iteration, a globally convergent variant of AA for DFPM named as AA-DFPM is proposed. Further, the linear convergence rate is proved under some mild assumptions. Experiments on both mathematical examples and a real-world application show encouraging results of AA-DFPM and confirm the suitability of AA for accelerating DFPM in solving optimization problems. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2403_14924 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Anderson acceleration of derivative-free projection methods for constrained monotone nonlinear equations Jin, Jiachen Wang, Hongxia Deng, Kangkang Optimization and Control The derivative-free projection method (DFPM) is an efficient algorithm for solving monotone nonlinear equations. As problems grow larger, there is a strong demand for speeding up the convergence of DFPM. This paper considers the application of Anderson acceleration (AA) to DFPM for constrained monotone nonlinear equations. By employing a nonstationary relaxation parameter and interleaving with slight modifications in each iteration, a globally convergent variant of AA for DFPM named as AA-DFPM is proposed. Further, the linear convergence rate is proved under some mild assumptions. Experiments on both mathematical examples and a real-world application show encouraging results of AA-DFPM and confirm the suitability of AA for accelerating DFPM in solving optimization problems. |
| title | Anderson acceleration of derivative-free projection methods for constrained monotone nonlinear equations |
| topic | Optimization and Control |
| url | https://arxiv.org/abs/2403.14924 |