- Linearized version of the generalized alternating direction method of multipliers for three-block separable convex minimization problem Zhang Xue-Qing (zxqcqspb163.com) Peng Jian-Wen (jwpeng168hotmail.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: 09/26/2017Entry Accepted: 09/26/2017Entry Last Modified: 09/26/2017Modify/Update this entry Visitors Authors More about us Links Subscribe, Unsubscribe Digest Archive Search, Browse the Repository Submit Update Policies Coordinator's Board Classification Scheme Credits Give us feedback Optimization Journals, Sites, Societies Optimization Online is supported by the Mathematical Optmization Society.