ON THE LINEAR CONVERGENCE RATE OF GENERALIZED ADMM FOR CONVEX COMPOSITE PROGRAMMING

被引：0
作者：
Wang, Han [1 ]
Li, Peili [2 ]
Xiao, Yunhai [2 ]
机构：
[1] School of Mathematics and Statistics, Henan University, Kaifeng
[2] Center for Applied Mathematics of Henan Province, Henan University, Kaifeng
来源：
Journal of Applied and Numerical Optimization | 2024年 / 6卷 / 01期
基金：
中国国家自然科学基金;
关键词：
Alternating direction method of multipliers; Calmness; Error bound condition; Linear convergence rate; Semi-proximal terms;
D O I：
10.23952/jano.6.2024.1.07
中图分类号：
学科分类号：
摘要：
Over the fast few years, the numerical success of the generalized alternating direction method of multipliers (GADMM) proposed by Eckstein and Bertsekas [Math. Progam. 1992] has inspired intensive attention in analyzing its theoretical convergence properties. This paper is devoted to 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. © 2024 Journal of Applied and Numerial Optimization.
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页码：115 / 134
页数：19
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