A Derivative-Free Saddle-search Algorithm With Linear Convergence Rate
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arXiv
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| Main Authors: | , , , |
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| Format: | Preprint |
| Published: |
2026
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| _version_ | 1866917186309718016 |
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| author | Du, Qiang Shi, Baoming Zhang, Lei Zheng, Xiangcheng |
| author_facet | Du, Qiang Shi, Baoming Zhang, Lei Zheng, Xiangcheng |
| contents | We propose a derivative-free saddle-search algorithm designed to locate transition states using only function evaluations. The algorithm employs a nested architecture consisting of an inner eigenvector search and an outer saddle-point search. Through rigorous numerical analysis, we prove the almost sure convergence of the inner step under suitable assumptions. Furthermore, we establish the convergence of the outer search using a decaying step size, while demonstrating linear convergence under constant step size and boundedness conditions. Numerical experiments are provided to validate our theoretical results and demonstrate the algorithm's practical applicability. |
| format | Preprint |
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arxiv_https___arxiv_org_abs_2601_02650 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | A Derivative-Free Saddle-search Algorithm With Linear Convergence Rate Du, Qiang Shi, Baoming Zhang, Lei Zheng, Xiangcheng Numerical Analysis Optimization and Control We propose a derivative-free saddle-search algorithm designed to locate transition states using only function evaluations. The algorithm employs a nested architecture consisting of an inner eigenvector search and an outer saddle-point search. Through rigorous numerical analysis, we prove the almost sure convergence of the inner step under suitable assumptions. Furthermore, we establish the convergence of the outer search using a decaying step size, while demonstrating linear convergence under constant step size and boundedness conditions. Numerical experiments are provided to validate our theoretical results and demonstrate the algorithm's practical applicability. |
| title | A Derivative-Free Saddle-search Algorithm With Linear Convergence Rate |
| topic | Numerical Analysis Optimization and Control |
| url | https://arxiv.org/abs/2601.02650 |