Distributed dual subgradient method with double averaging: Application to QoS optimization in wireless networks

This work addresses multi-agent optimization problems with decoupled local objective functions and coupled inequality constraints. A distributed dual subgradient method with double averaging that is built on the dual decomposition, the subgradient method with double averaging, and the dynamic average consensus is developed to solve the global problem with only local computation and peer-to-peer communication. It is theoretically proved that, for the primal-dual sequence, both the dual objective error and the quadratic penalty for the coupled constraints have $O\left( {\frac{1}{{\sqrt t }}} \right)$ upper bounds, and the primal objective error asymptotically vanishes. The proposed algorithm is applied to optimize the Quality of Service (QoS) in wireless networks; numerical results verify the effectiveness of the proposed algorithm.