Model-Driven Subspaces for Large-Scale Optimization with Local Approximation Strategy
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arXiv
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| Format: | Preprint |
| Published: |
2025
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| _version_ | 1866908529899601920 |
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| author | He, Yitong Xie, Pengcheng |
| author_facet | He, Yitong Xie, Pengcheng |
| contents | Solving large-scale optimization problems is a bottleneck and is very important for machine learning and multiple kinds of scientific problems. Subspace-based methods using the local approximation strategy are one of the most important methods. This paper discusses different and novel kinds of advanced subspaces for such methods and presents a new algorithm with such subspaces, called MD-LAMBO. Theoretical analysis including the subspaces' properties, sufficient function value decrease, and global convergence is given for the new algorithm. The related model construction on the subspaces is given under derivative-free settings. In numerical results, performance profiles, and truncated Newton step errors of MD-LAMBO using different model-driven subspaces are provided, which show subspace-dependent numerical differences and advantages of our methods and subspaces. |
| format | Preprint |
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arxiv_https___arxiv_org_abs_2509_08256 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Model-Driven Subspaces for Large-Scale Optimization with Local Approximation Strategy He, Yitong Xie, Pengcheng Optimization and Control Numerical Analysis 90C26, 90C30, 65K05, 49M37 Solving large-scale optimization problems is a bottleneck and is very important for machine learning and multiple kinds of scientific problems. Subspace-based methods using the local approximation strategy are one of the most important methods. This paper discusses different and novel kinds of advanced subspaces for such methods and presents a new algorithm with such subspaces, called MD-LAMBO. Theoretical analysis including the subspaces' properties, sufficient function value decrease, and global convergence is given for the new algorithm. The related model construction on the subspaces is given under derivative-free settings. In numerical results, performance profiles, and truncated Newton step errors of MD-LAMBO using different model-driven subspaces are provided, which show subspace-dependent numerical differences and advantages of our methods and subspaces. |
| title | Model-Driven Subspaces for Large-Scale Optimization with Local Approximation Strategy |
| topic | Optimization and Control Numerical Analysis 90C26, 90C30, 65K05, 49M37 |
| url | https://arxiv.org/abs/2509.08256 |