Hard-thresholding-based algorithms have seen various advantages for sparse optimization in controlling the sparsity and allowing for fast computation. Recent research shows that when techniques of the Newton-type methods are integrated, their numerical performance can be improved surprisingly. This paper develops a gradient projection Newton pursuit algorithm that mainly adopts the hard-thresholding operator and employs the Newton pursuit only when certain conditions are satisfied. The proposed algorithm is capable of converging globally and quadratically under the standard assumptions. When it comes to compressive sensing problems, the imposed assumptions are much weaker than those for many state-of-the-art algorithms. Moreover, extensive numerical experiments have demonstrated its high performance in comparison with the other leading solvers.

基于硬阈值的算法已经看到了稀疏优化在控制稀疏性和允许快速计算方面的各种优势。最近的研究表明，当整合牛顿型方法的技术时，它们的数值性能可以得到惊人的提高。本文开发了一种梯度投影牛顿追踪算法，该算法主要采用硬阈值算子，只有在满足一定条件时才采用牛顿追踪。所提出的算法能够在标准假设下全局收敛和二次收敛。当谈到压缩感知问题时，强加的假设比许多最先进算法的假设要弱得多。此外，与其他领先的求解器相比，大量的数值实验证明了它的高性能。