自适应惯性集成时变近端ADMM算法  

Adaptive Inertia Integrated Time-Varying Proximal Alternating Direction Method of Multipliers (ADMM) Algorithm

作　　者：薛中会 孙志远 霍利婷 

机构地区：[1]上海出版印刷高等专科学校,信息与智能工程系,上海 [2]上海出版印刷高等专科学校,马克思主义学院,上海

出　　处：《理论数学》2024年第9期16-29,共14页Pure Mathematics

摘　　要：本文提出了一种自适应惯性时变近端ADMM方法,旨在解决具有挑战性的非凸优化问题。该方法通过自适应调整惯性项和近端参数,增强了算法对非凸性和复杂结构的适应能力。我们的理论分析证明了在合适的条件下,算法能够实现全局收敛。数值实验部分展示了该方法在多个非凸优化问题上的有效性,包括稀疏信号恢复和图像处理任务。This paper proposes an adaptive inertial time-varying proximal ADMM method aimed at tackling challenging non-convex optimization problems. By adaptively adjusting the inertial term and proximal parameters, the algorithm enhances its adaptability to non-convexity and complex structures. Our theoretical analysis proves that the algorithm can achieve global convergence under suitable conditions. The numerical experiments demonstrate the effectiveness of this method on multiple non-convex optimization problems, including sparse signal recovery and image processing tasks.

关 键 词：交替方向乘子法(ADMM) 自适应惯性项 时变近端策略 

分 类 号：TP3[自动化与计算机技术—计算机科学与技术]