带有保护条件的ν加速ADMM算法

ν-Accelerated ADMM Algorithm with Safe Guard Conditions

摘要: 本文提出了一种结合L₁ − L₂正则化和ν加速的交替方向乘子法(ADMM)，用于解决稀疏信号恢复问题。本文基于L₁ − L₂正则化的近端算子解析解，提出了一种带有保护机条件的ν加速ADMM算法(νADMMgd)。该算法通过引入ν加速技术，显著提高了收敛速度，并通过保护机制确保了算法的稳定性。数值实验表明，νADMMgd算法在稀疏信号恢复问题上表现出色，能够在较短时间内达到更优的函数值，且在处理大规模数据时具有较高的计算效率。实验还验证了该算法在不同稀疏度和正则化参数下的鲁棒性。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，尤其是在高维数据和大规模优化问题中表现尤为突出。

Abstract: This paper proposes a novel Alternating Direction Method of Multipliers (ADMM) combined with L₁ − L₂ regularization and ν-acceleration for solving sparse signal recoveryproblems. Based on the analytical solution of the proximal operator for L₁ − L₂ regularization, we introduce a ν-accelerated ADMM algorithm with safeguard conditions(νADMMgd). This algorithm significantly enhances the convergence speed by incorporating ν-acceleration techniques and ensures stability through safeguard mechanisms. Numerical experiments demonstrate that the νADMMgd algorithm performs excellently in sparse signal recovery, achieving superior function values in a shorter time and exhibiting high computational efficiency when handling large-scale data. The experiments also validate the robustness of the algorithm under different sparsity levels and regularization parameters. Overall, the proposed algorithm shows significant advantages in sparse signal recovery problems, particularly in high-dimensional data and large-scale optimization scenarios.