An Optimal Interpolation Set for Model-Based Derivative-Free Optimization Methods
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arXiv
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| Hauptverfasser: | , |
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| Format: | Preprint |
| Veröffentlicht: |
2023
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| _version_ | 1866909340484501504 |
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| author | Ragonneau, Tom M. Zhang, Zaikun |
| author_facet | Ragonneau, Tom M. Zhang, Zaikun |
| contents | This paper demonstrates the optimality of an interpolation set employed in derivative-free trust-region methods. This set is optimal in the sense that it minimizes the constant of well-poisedness in a ball centred at the starting point. It is chosen as the default initial interpolation set by many derivative-free trust-region methods based on underdetermined quadratic interpolation, including NEWUOA, BOBYQA, LINCOA, and COBYQA. Our analysis provides a theoretical justification for this choice. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2302_09992 |
| institution | arXiv |
| publishDate | 2023 |
| record_format | arxiv |
| spellingShingle | An Optimal Interpolation Set for Model-Based Derivative-Free Optimization Methods Ragonneau, Tom M. Zhang, Zaikun Optimization and Control 90C56, 41A10, 65K05, 90C30 This paper demonstrates the optimality of an interpolation set employed in derivative-free trust-region methods. This set is optimal in the sense that it minimizes the constant of well-poisedness in a ball centred at the starting point. It is chosen as the default initial interpolation set by many derivative-free trust-region methods based on underdetermined quadratic interpolation, including NEWUOA, BOBYQA, LINCOA, and COBYQA. Our analysis provides a theoretical justification for this choice. |
| title | An Optimal Interpolation Set for Model-Based Derivative-Free Optimization Methods |
| topic | Optimization and Control 90C56, 41A10, 65K05, 90C30 |
| url | https://arxiv.org/abs/2302.09992 |