In this paper, we propose and evaluate a new communication-efficient design technique for solving the linear quadratic regulator (LQR) optimal control problem. We propose this design to minimize the communication overhead and resulting energy consumption in wireless distributed control scenarios in the context of cooperative vehicular networking (CVN). We introduce the LQR optimal control design problem, then we propose our new design technique using the alternating direction method of multipliers (ADMM). Our numerical results demonstrate that our communication-efficient control design can outperform the previous methods namely the sparsity-promoting optimal control design and the conventional LQR optimal control design. We also provide simulation results to evaluate the resilience of proposed technique under various wireless connectivity conditions.