# Newton-Type Optimal Thresholding Algorithms for Sparse Optimization Problems

arXiv: https://arxiv.org/abs/2104.02371 · HTML: https://mlsanity.com/paper/2104.02371/

## Key facts

- Cited by 1 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 6 Apr 2021.

## Built on by (most cited first, 1 of 1)

- [Evolutionary Feature-wise Thresholding for Binary Representation of NLP Embeddings](https://mlsanity.com/paper/2507.17025/) (2025)

## Abstract (arXiv)

Sparse signals can be possibly reconstructed by an algorithm which merges a traditional nonlinear optimization method and a certain thresholding technique. Different from existing thresholding methods, a novel thresholding technique referred to as the optimal k-thresholding was recently proposed by Zhao [SIAM J Optim, 30(1), pp. 31-55, 2020]. This technique simultaneously performs the minimization of an error metric for the problem and thresholding of the iterates generated by the classic gradient method. In this paper, we propose the so-called Newton-type optimal k-thresholding (NTOT) algorithm which is motivated by the appreciable performance of both Newton-type methods and the optimal k-thresholding technique for signal recovery. The guaranteed performance (including convergence) of the proposed algorithms are shown in terms of suitable choices of the algorithmic parameters and the restricted isometry property (RIP) of the sensing matrix which has been widely used in the analysis of compressive sensing algorithms. The simulation results based on synthetic signals indicate that the proposed algorithms are stable and efficient for signal recovery.