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Linearized version of the generalized alternating direction method of multipliers for three-block separable convex minimization problem

Zhang Xue-Qing (zxqcqspb***at***163.com)
Peng Jian-Wen (jwpeng168***at***hotmail.com)

Abstract: Recently, the generalized alternating direction method of multipliers (GADMM) proposed by Eckstein and Bertsekas has received wide attention, especially with respect to numerous applications. In this paper, we develop a new linearized version of generalized alternating direction method of multipliers (L-GADMM) for the linearly constrained separable convex programming whose objective functions are the sum of three convex functions without coupled variables. We give a sufficient condition to ensure the convergence of the L-GADMM for three-block separable convex minimization problem. Theoretically, we establish the worst-case $\mathcal{O}(1/t)$ convergence rate for the proposed L-GADMM in both ergodic and nonergodic senses under the sufficient condition. Moreover, we also show an example to prove its divergence of the proposed L-GADMM if the sufficient condition is lost and give some numerical results.

Keywords: The linearized version of generalized alternating direction method of multipliers; Convergence; Three-block separable convex minimization problem; Matrix optimization problem.

Category 1: Convex and Nonsmooth Optimization (Convex Optimization )

Citation: Sept. 26, 2017

Download: [PDF]

Entry Submitted: 09/26/2017
Entry Accepted: 09/26/2017
Entry Last Modified: 09/26/2017

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