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Han Wang, Peili Li, Yunhai Xiao, On the linear convergence rate of generalized ADMM for convex composite programming

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DOI: 10.23952/jano.6.2024.1.07
Volume 6, Issue 1, 1 April 2024, Pages 115-134

 

Abstract. Over the fast few years, the numerical success of the generalized alternating direction method of multipliers (GADMM) proposed by Eckstein and Bertsekas [Math. Program. 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.

 

How to Cite this Article:
H. Wang, P. Li, Y. Xiao, On the linear convergence rate of generalized ADMM for convex composite programming, J. Appl. Numer. Optim. 6 (2024), 115-134.