论文标题
关于凸复合编程的广义ADMM的线性收敛速率
On the Linear Convergence Rate of Generalized ADMM for Convex Composite Programming
论文作者
论文摘要
在迅速的几年中，Eckstein \＆Bertsekas提出的乘数（GADMM）的广义交替方向方法的数值成功[Math。 Prog。，1992]激发了分析其理论收敛特性的密集关注。在本文中，我们致力于建立半耐gadmm（SPGADMM）的线性收敛速率，以解决线性约束的凸复合优化问题。每个子问题中包含的半高术语具有有效处理多块问题的能力。我们最初对SPGADMM产生的序列提出了一些重要的不平等，然后在镇静的假设下建立局部线性收敛速率。作为副产品，还讨论了全球收敛属性。
Over the fast few years, the numerical success of the generalized alternating direction method of multipliers (GADMM) proposed by Eckstein \& Bertsekas [Math. Prog., 1992] has inspired intensive attention in analyzing its theoretical convergence properties. In this paper, we devote to establishing the linear convergence rate of the semi-proximal GADMM (sPGADMM) for solving linearly constrained convex composite optimization problems. The semi-proximal terms contained in each subproblem possess the abilities of handling with multi-block problems efficiently. We initially present some important inequalities for the sequence generated by the sPGADMM, and then establish the local linear convergence rate under the assumption of calmness. As a by-product, the global convergence property is also discussed.
