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

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.

Sept. 26, 2017