Scalable Derivative-Free Optimization Algorithms with Low-Dimensional Subspace Techniques
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arXiv
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| Format: | Preprint |
| Publié: |
2025
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| _version_ | 1866910777157353472 |
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| author | Zhang, Zaikun |
| author_facet | Zhang, Zaikun |
| contents | We re-introduce a derivative-free subspace optimization framework originating from Chapter 5 of the Ph.D. thesis [Z. Zhang, On Derivative-Free Optimization Methods, Ph.D. thesis, Chinese Academy of Sciences, Beijing, 2012] of the author under the supervision of Ya-xiang Yuan. At each iteration, the framework defines a (low-dimensional) subspace based on an approximate gradient, and then solves a subproblem in this subspace to generate a new iterate. We sketch the global convergence and worst-case complexity analysis of the framework, elaborate on its implementation, and present some numerical results on solving problems with dimensions as high as 10^4 using only inaccurate function values. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2501_04536 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Scalable Derivative-Free Optimization Algorithms with Low-Dimensional Subspace Techniques Zhang, Zaikun Optimization and Control We re-introduce a derivative-free subspace optimization framework originating from Chapter 5 of the Ph.D. thesis [Z. Zhang, On Derivative-Free Optimization Methods, Ph.D. thesis, Chinese Academy of Sciences, Beijing, 2012] of the author under the supervision of Ya-xiang Yuan. At each iteration, the framework defines a (low-dimensional) subspace based on an approximate gradient, and then solves a subproblem in this subspace to generate a new iterate. We sketch the global convergence and worst-case complexity analysis of the framework, elaborate on its implementation, and present some numerical results on solving problems with dimensions as high as 10^4 using only inaccurate function values. |
| title | Scalable Derivative-Free Optimization Algorithms with Low-Dimensional Subspace Techniques |
| topic | Optimization and Control |
| url | https://arxiv.org/abs/2501.04536 |