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...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.展开更多
文摘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.
