Randomized Subspace Derivative-Free Optimization with Quadratic Models and Second-Order Convergence
Fuente:
arXiv
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| Autori principali: | , |
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| Natura: | Preprint |
| Pubblicazione: |
2024
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| _version_ | 1866916532509999104 |
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| author | Cartis, Coralia Roberts, Lindon |
| author_facet | Cartis, Coralia Roberts, Lindon |
| contents | We consider model-based derivative-free optimization (DFO) for large-scale problems, based on iterative minimization in random subspaces. We provide the first worst-case complexity bound for such methods for convergence to approximate second-order critical points, and show that these bounds have significantly improved dimension dependence compared to standard full-space methods, provided low accuracy solutions are desired and/or the problem has low effective rank. We also introduce a practical subspace model-based method suitable for general objective minimization, based on iterative quadratic interpolation in subspaces, and show that it can solve significantly larger problems than state-of-the-art full-space methods, while also having comparable performance on medium-scale problems when allowed to use full-dimension subspaces. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2412_14431 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Randomized Subspace Derivative-Free Optimization with Quadratic Models and Second-Order Convergence Cartis, Coralia Roberts, Lindon Optimization and Control We consider model-based derivative-free optimization (DFO) for large-scale problems, based on iterative minimization in random subspaces. We provide the first worst-case complexity bound for such methods for convergence to approximate second-order critical points, and show that these bounds have significantly improved dimension dependence compared to standard full-space methods, provided low accuracy solutions are desired and/or the problem has low effective rank. We also introduce a practical subspace model-based method suitable for general objective minimization, based on iterative quadratic interpolation in subspaces, and show that it can solve significantly larger problems than state-of-the-art full-space methods, while also having comparable performance on medium-scale problems when allowed to use full-dimension subspaces. |
| title | Randomized Subspace Derivative-Free Optimization with Quadratic Models and Second-Order Convergence |
| topic | Optimization and Control |
| url | https://arxiv.org/abs/2412.14431 |