A penalty ADMM with quantized communication for distributed optimization over multi-agent systems

summary:In this paper, we design a distributed penalty ADMM algorithm with quantized communication to solve distributed convex optimization problems over multi-agent systems. Firstly, we introduce a quantization scheme that reduces the bandwidth limitation of multi-agent systems without requiring an encoder or decoder, unlike existing quantized algorithms. This scheme also minimizes the computation burden. Moreover, with the aid of the quantization design, we propose a quantized penalty ADMM to obtain the suboptimal solution. Furthermore, the proposed algorithm converges to the suboptimal solution with an $O(\frac{1}{k})$ convergence rate for general convex objective functions, and with an R-linear rate for strongly convex objective functions