We study energy-efficient decentralized coordinated beamforming in multi-cell multiuser multiple-input single-output system. The problem of interest is to maximize the weighted sum energy efficiency subject to user-specific quality of service constraints. The original problem is iteratively approximated as a convex program according to successive convex approximation (SCA) principle. The convex problem at each iteration is then formulated as a general global
consensus problem, which is solved via alternating direction method of multipliers (ADMM). This enables base stations to independently and in parallel optimize their beamformers relying only on local channel state information and limited backhaul information exchange. In addition to waiting for the ADMM to converge as conventionally when solving the approximate convex program, we propose a method where only one ADMM iteration is performed after each SCA update step. Numerical results illustrate the fast convergence of the proposed methods and show that performing only one ADMM iteration per each convex problem can significantly improve the convergence speed.