对数和正则化的带保护条件的加速ADMM算法

Log-Sum Accelerated ADMM Algorithm with Protection Conditions

摘要: 本文针对稀疏信号恢复问题，提出了一种基于对数和正则化模型的带有保护条件的Nesterov加速ADMM算法(nADMMgd)。该算法通过引入Nesterov加速技术有效提高了收敛速率，并利用保护条件保障了算法的稳定性。数值实验表明，nADMMgd算法在稀疏信号恢复问题上表现出色，能够在较短的时间内达到更优的函数值，且在计算大规模数据时具有良好的表现。实验验证了保护条件对计算效率方面提升的积极作用，还验证了nADMMgd对比目前用于计算对数和正则化的算法得到的结果更加精确。总体而言，本文提出的算法在稀疏信号恢复问题中具有显著的优势。

Abstract: This paper proposes a Nesterov-accelerated ADMM algorithm with protection conditions, referred to as nADMMgd, for sparse signal recovery based on logarithmic and regularization models. By incorporating Nesterov acceleration techniques, the algorithm achieves an improved convergence rate, while the integration of protective conditions enhances its numerical stability. Numerical experiments demonstrate that nADMMgd performs effectively in sparse signal recovery tasks, attaining superior objective function values within reduced computational time and exhibiting robust performance on large-scale datasets. The experimental results confirm the positive impact of the protective conditions on computational efficiency and further validate that nADMMgd yields more accurate solutions compared to state-of-the-art algorithms currently employed for logarithmic and regularized optimization. Overall, the proposed method presents significant advantages in addressing sparse signal recovery problems.