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PreprintCC BY 4.0arXiv

Sparse descent subspace-Newton thresholding algorithm for sparse optimization problems

  • Zhong-Feng Sun
  • Nan Meng
  • Yun-Bin Zhao
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Abstract

In this paper, we propose a sparse descent direction derived from the Newton direction within a low-dimensional subspace for sparse optimization problems. Building upon this direction and incorporating hard thresholding and orthogonal projection, we develop a novel algorithm termed the sparse descent subspace-Newton thresholding (SDSNT) algorithm. We further establish its global convergence under the restricted isometry property δ3k≤ √(3/20) of the measurement matrix. Numerical experiments on random sparse vector recovery and audio signal reconstruction reveal that SDSNT achieves comparable performance to several state-of-the-art algorithms. Notably, relative to most of them, it delivers superior recovery at high sparsity levels and improved efficiency at low sparsity levels.

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Cite

BibTeXRIS
BibTeX
@misc{sun2026sparse,
  title = {{Sparse descent subspace-Newton thresholding algorithm for sparse optimization problems}},
  author = {Zhong-Feng Sun and Nan Meng and Yun-Bin Zhao},
  howpublished = {arXiv},
  year = {2026},
  month = oct,
  doi = {10.48550/arxiv.2610.41318},
  eprint = {2610.41318},
  archivePrefix = {arXiv},
  url = {https://arxiv.org/abs/2610.41318},
  note = {CC BY 4.0},
}
RIS
TY  - UNPB
TI  - Sparse descent subspace-Newton thresholding algorithm for sparse optimization problems
AU  - Zhong-Feng Sun
AU  - Nan Meng
AU  - Yun-Bin Zhao
PY  - 2026
DA  - 2026/10/30
PB  - arXiv
DO  - 10.48550/arxiv.2610.41318
UR  - https://arxiv.org/abs/2610.41318
AB  - In this paper, we propose a sparse descent direction derived from the Newton direction within a low-dimensional subspace for sparse optimization problems. Building upon this direction and incorporating hard thresholding and orthogonal projection, we develop a novel algorithm termed the sparse descent subspace-Newton thresholding (SDSNT) algorithm. We further establish its global convergence under the restricted isometry property δ_3k≤ √(3/20) of the measurement matrix. Numerical experiments on random sparse vector recovery and audio signal reconstruction reveal that SDSNT achieves comparable performance to several state-of-the-art algorithms. Notably, relative to most of them, it delivers superior recovery at high sparsity levels and improved efficiency at low sparsity levels.
ER  -