Year: 2025
Type: preprint
Abstract: Thresholding algorithms for sparse optimization problems involve two key components: search directions and thresholding strategies. In this paper, we use the compressed Newton direction as a search direction, derived by confining the classical Newton step to a low-dimensional subspace and embedding it back into the full space with diagonal regularization. This approach significantly reduces the computational cost for finding the search direction while maintaining the efficiency of Newton-like methods. Based on this new search direction, we propose two major classes of algorithms by adopting hard or optimal thresholding: the compressed Newton-direction-based thresholding pursuit (CNHTP) and compressed Newton-direction-based optimal thresholding pursuit (CNOTP). We establish the global convergence of the proposed algorithms under the restricted isometry property. Experimental results demonstrate that the proposed algorithms perform comparably to several state-of-the-art methods in terms of success frequency and solution accuracy for solving the sparse optimization problem.
Source: arXiv (Cornell University)
Authors: Meng, Nan, Zhao, Yun-Bin
Language: English
Subfield: Computational Mechanics
Field: Engineering
Domain: Physical Sciences
Open Access status: green
Awards: G332846087, G3650404787
OpenAlex ID: W4416330288
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