A Fast and Convergent Algorithm for Unassigned Distance Geometry Problems

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Détails bibliographiques
Auteurs principaux:	Fan, Jun, Shan, Xiaoya, Xiu, Xianchao
Format:	Preprint
Publié:	2025
Sujets:	Optimization and Control
Accès en ligne:	Acceder al recurso
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_version_	1866908610512027648
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

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