A Fast and Convergent Algorithm for Unassigned Distance Geometry Problems

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.

• Publication year

  2025

• Venue

  Unknown venue

• Publication date

  2025-02-04

• Fields of study

  Mathematics

• Identifiers
  arXiv 2502.02280
• External record

  Open on Semantic Scholar

• Source metadata

  Semantic Scholar

• No claims are published for this paper.

• No concepts are published for this paper.

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