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| Main Authors: | , |
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| Format: | Preprint |
| Published: |
2025
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| Subjects: | |
| Online Access: | https://arxiv.org/abs/2506.21948 |
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| _version_ | 1866915443091963904 |
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| author | Liu, Yichuan Li, Yingzhou |
| author_facet | Liu, Yichuan Li, Yingzhou |
| contents | We propose UPOQA, a derivative-free optimization algorithm for partially separable unconstrained problems, leveraging quadratic interpolation and a structured trust-region framework. By decomposing the objective into element functions, UPOQA constructs underdetermined element models and solves subproblems efficiently via a modified projected gradient method. Innovations include an approximate projection operator for structured trust regions, improved management of elemental radii and models, a starting point search mechanism, and support for hybrid black-white-box optimization, etc. Numerical experiments on 85 CUTEst problems demonstrate that \texttt{UPOQA} can significantly reduce the number of function evaluations. To quantify the impact of exploiting partial separability, we introduce the speed-up profile to further evaluate the acceleration effect. Results show that the speed-up of UPOQA over baselines is less significant in low-precision scenarios but becomes more pronounced in high-precision scenarios. Applications to quantum variational problems further validate its practical utility. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2506_21948 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | A Model-Based Derivative-Free Optimization Algorithm for Partially Separable Problems Liu, Yichuan Li, Yingzhou Optimization and Control We propose UPOQA, a derivative-free optimization algorithm for partially separable unconstrained problems, leveraging quadratic interpolation and a structured trust-region framework. By decomposing the objective into element functions, UPOQA constructs underdetermined element models and solves subproblems efficiently via a modified projected gradient method. Innovations include an approximate projection operator for structured trust regions, improved management of elemental radii and models, a starting point search mechanism, and support for hybrid black-white-box optimization, etc. Numerical experiments on 85 CUTEst problems demonstrate that \texttt{UPOQA} can significantly reduce the number of function evaluations. To quantify the impact of exploiting partial separability, we introduce the speed-up profile to further evaluate the acceleration effect. Results show that the speed-up of UPOQA over baselines is less significant in low-precision scenarios but becomes more pronounced in high-precision scenarios. Applications to quantum variational problems further validate its practical utility. |
| title | A Model-Based Derivative-Free Optimization Algorithm for Partially Separable Problems |
| topic | Optimization and Control |
| url | https://arxiv.org/abs/2506.21948 |