论文标题
与应用的放松惯性交流算法的收敛分析
Convergence analysis of a relaxed inertial alternating minimization algorithm with applications
论文作者
论文摘要
乘数的交替方向方法（ADMM）是一种通过线性平等约束解决凸的可分离最小化问题的流行方法。两个块ADMM对三个块ADMM的概括不是微不足道的，因为三个块ADMM一般不是融合。已经开发了许多三个块ADMM的变体，并保证收敛。除ADMM外，交替的最小化算法（AMA）也是通过线性等效约束解决凸的可分离最小化问题的重要算法。 AMA首先是由Tseng提出的，它等同于应用于相应的双重问题的前向后分裂算法。在本文中，我们设计了三个块AMA的变体，该变体是通过使用三个操作员分裂算法的惯性扩展来得出的。与三个块ADMM相比，所提出的算法的第一个子问题仅最大程度地减少拉格朗日函数。作为副产品，我们获得了戴维斯和阴的轻松算法。在参数的轻度条件下，我们建立了无限二维希尔伯特空间中提出的算法的收敛性。最后，我们对稳定的主成分追求（SPCP）进行数值实验，以验证所提出算法的效率和有效性。
The alternating direction method of multipliers (ADMM) is a popular method for solving convex separable minimization problems with linear equality constraints. The generalization of the two-block ADMM to the three-block ADMM is not trivial since the three-block ADMM is not convergence in general. Many variants of three-block ADMM have been developed with guarantee convergence. Besides the ADMM, the alternating minimization algorithm (AMA) is also an important algorithm for solving the convex separable minimization problem with linear equality constraints. The AMA is first proposed by Tseng, and it is equivalent to the forward-backward splitting algorithm applied to the corresponding dual problem. In this paper, we design a variant of three-block AMA, which is derived by employing an inertial extension of the three-operator splitting algorithm to the dual problem. Compared with three-block ADMM, the first subproblem of the proposed algorithm only minimizing the Lagrangian function. As a by-product, we obtain a relaxed algorithm of Davis and Yin. Under mild conditions on the parameters, we establish the convergence of the proposed algorithm in infinite-dimensional Hilbert spaces. Finally, we conduct numerical experiments on the stable principal component pursuit (SPCP) to verify the efficiency and effectiveness of the proposed algorithm.
