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.
Citation
Sept. 26, 2017