A Fast and Convergent Algorithm for Unassigned Distance Geometry Problems
Fuente:
arXiv
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| Autori principali: | , , |
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| Natura: | Preprint |
| Pubblicazione: |
2025
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| _version_ | 1866908610512027648 |
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| author | Fan, Jun Shan, Xiaoya Xiu, Xianchao |
| author_facet | Fan, Jun Shan, Xiaoya Xiu, Xianchao |
| contents | In this paper, we propose a fast and convergent algorithm to solve unassigned distance geometry problems (uDGP). Technically, we construct a novel quadratic measurement model by leveraging $\ell_0$-norm instead of $\ell_1$-norm in the literature. To solve the nonconvex model, we establish its optimality conditions and develop a fast iterative hard thresholding (IHT) algorithm. Theoretically, we rigorously prove that the whole generated sequence converges to the L-stationary point with the help of the Kurdyka-Lojasiewicz (KL) property. Numerical studies on the turnpike and beltway problems validate its superiority over existing $\ell_1$-norm-based method. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2502_02280 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | A Fast and Convergent Algorithm for Unassigned Distance Geometry Problems Fan, Jun Shan, Xiaoya Xiu, Xianchao Optimization and Control In this paper, we propose a fast and convergent algorithm to solve unassigned distance geometry problems (uDGP). Technically, we construct a novel quadratic measurement model by leveraging $\ell_0$-norm instead of $\ell_1$-norm in the literature. To solve the nonconvex model, we establish its optimality conditions and develop a fast iterative hard thresholding (IHT) algorithm. Theoretically, we rigorously prove that the whole generated sequence converges to the L-stationary point with the help of the Kurdyka-Lojasiewicz (KL) property. Numerical studies on the turnpike and beltway problems validate its superiority over existing $\ell_1$-norm-based method. |
| title | A Fast and Convergent Algorithm for Unassigned Distance Geometry Problems |
| topic | Optimization and Control |
| url | https://arxiv.org/abs/2502.02280 |