论文标题
梯度投影牛顿追求稀疏性的优化
Gradient Projection Newton Pursuit for Sparsity Constrained Optimization
论文作者
论文摘要
基于硬质的算法在控制稀疏性和允许快速计算方面具有稀疏优化的各种优势。最近的研究表明，当整合牛顿型方法的技术时，它们的数值性能就可以令人惊讶地提高。本文开发了一种梯度投影牛顿追求算法，该算法主要采用势头限额操作员，并仅在满足某些条件时才采用牛顿追求。所提出的算法能够在标准假设下全球和四次收敛。当涉及到压缩感知问题时，对许多最新算法的假设比那些弱的假设要弱得多。此外，与其他领先求解器相比，广泛的数值实验证明了其高性能。
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.
