On the Linear Convergence Rate of Generalized ADMM for Convex Composite Programming

2022/06/08 by Wang, Han, Li, Peili, Xiao, Yunhai
#FOS: Mathematics #Optimization and Control (math.OC)

paper · doi:10.48550/arxiv.2206.03649

Abstract

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.

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