Title: Compressed Newton-direction-based Thresholding Methods for Sparse Optimization Problems Show Chinese title

Title: 基于压缩牛顿方向的阈值方法用于稀疏优化问题

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. Show Chinese abstract

Abstract: 阈值算法用于稀疏优化问题包含两个关键组成部分：搜索方向和阈值策略。 在本文中，我们使用压缩牛顿方向作为搜索方向，该方向通过将经典牛顿步限制在低维子空间并以对角线正则化将其嵌入全空间得到。 这种方法显著降低了寻找搜索方向的计算成本，同时保持了类似牛顿方法的效率。 基于这种新的搜索方向，我们通过采用硬阈值或最优阈值提出了两种主要算法类：基于压缩牛顿方向的阈值追逐（CNHTP）和基于压缩牛顿方向的最优阈值追逐（CNOTP）。 我们在受限等距性质下建立了所提出算法的全局收敛性。 实验结果表明，所提出的算法在解决稀疏优化问题的成功频率和解的准确性方面与几种最先进的方法表现相当。