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
针对粒子群算法(Particle Swarm Optimization,PSO)易陷入局部极值的缺陷,提出了一种新的自适应惯性权重混沌PSO算法(a New Chaos Particle Swarm Optimization based on Adaptive Inertia Weight,CPSO-NAIW)。首先采用新的惯性权重自...针对粒子群算法(Particle Swarm Optimization,PSO)易陷入局部极值的缺陷,提出了一种新的自适应惯性权重混沌PSO算法(a New Chaos Particle Swarm Optimization based on Adaptive Inertia Weight,CPSO-NAIW)。首先采用新的惯性权重自适应方法,很好地平衡粒子的搜索行为,减少算法陷入局部极值的概率,然后在算法陷入局部极值时,引入混沌优化策略,对群体极值位置进行调整,以使粒子搜索新的邻域和路径,增加算法摆脱局部极值的可能。最后,实验结果表明,CPSO-NAIW算法能有效避免陷入局部极值,提高算法性能。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.
文摘针对粒子群算法(Particle Swarm Optimization,PSO)易陷入局部极值的缺陷,提出了一种新的自适应惯性权重混沌PSO算法(a New Chaos Particle Swarm Optimization based on Adaptive Inertia Weight,CPSO-NAIW)。首先采用新的惯性权重自适应方法,很好地平衡粒子的搜索行为,减少算法陷入局部极值的概率,然后在算法陷入局部极值时,引入混沌优化策略,对群体极值位置进行调整,以使粒子搜索新的邻域和路径,增加算法摆脱局部极值的可能。最后,实验结果表明,CPSO-NAIW算法能有效避免陷入局部极值,提高算法性能。
