Complete distributed optimization with constraints on networked multi-agent systems and its application to real-time pricing

This paper deals with a distributed constraint optimization problem on networked multi-agent systems. First, we propose a complete distributed algorithm based on the Lagrangian method which does not rely on supervisors. A new method to estimate the Lagrangian multiplier is proposed which enables each agent to obtain the Lagrangian multiplier in a distributed manner. Next, we derive a necessary and sufficient condition that the optimization problem is solvable in a distributed manner over a given network. Finally, a numerical example illustrates the effectiveness of the proposed method.