Quantized ADMM design for distributed strongly convex optimization

This paper proposes a novel quantized alternating direction method of multipliers (ADMM) for distributed optimization problems where the strongly convex objective function contains smooth and non-smooth parts. When the objective function is strongly convex and smooth, we show that the proposed quantized ADMM converges to an exact solution with an R-linearly convergent rate. We also present that the proposed algorithm converges to a more accurate solution than that of existing optimization algorithms with a fixed quantization interval if the objective function is strongly convex and non-smooth. Moreover, the convergent performance and the computation complexity of the proposed algorithm are analyzed. Finally, we provide two numerical examples to illustrate the effectiveness of the proposed algorithm.