  Privacy issues and communication cost are both major concerns in distributed
optimization. There is often a trade-off between them because the encryption
methods required for privacy-preservation often incur expensive communication
bandwidth. To address this issue, we, in this paper, propose a
quantization-based approach to achieve both communication efficient and
privacy-preserving solutions in the context of distributed optimization. By
deploying an adaptive differential quantization scheme, we allow each node in
the network to achieve its optimum solution with a low communication cost while
keeping its private data unrevealed. Additionally, the proposed approach is
general and can be applied in various distributed optimization methods, such as
the primal-dual method of multipliers (PDMM) and the alternating direction
method of multipliers (ADMM). Moveover, we consider two widely used adversary
models: passive and eavesdropping. Finally, we investigate the properties of
the proposed approach using different applications and demonstrate its superior
performance in terms of several parameters including accuracy, privacy, and
communication cost.
