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
DOI: 10.12677/pm.2024.149322, PDF,   
作者: 薛中会, 孙志远：上海出版印刷高等专科学校，信息与智能工程系，上海；霍利婷：上海出版印刷高等专科学校，马克思主义学院，上海
关键词: 交替方向乘子法(ADMM)；自适应惯性项；时变近端策略；Alternating Direction Method of Multipliers (ADMM)； Adaptive Inertia Term； Time-Varying Proximal Strategy
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。
Abstract: 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.
文章引用：薛中会, 孙志远, 霍利婷. 自适应惯性集成时变近端ADMM算法[J]. 理论数学, 2024, 14(9): 16-29. https://doi.org/10.12677/pm.2024.149322

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