  We consider a class of multi-agent optimization problems, where each agent
has a local objective function that depends on its own decision variables and
the aggregate of others, and is willing to cooperate with other agents to
minimize the sum of the local objectives. After associating each agent with an
auxiliary variable and the related local estimates, we conduct primal
decomposition to the globally coupled problem and reformulate it so that it can
be solved distributedly. Based on the Douglas-Rachford method, an algorithm is
proposed which ensures the exact convergence to a solution of the original
problem. The proposed method enjoys desirable scalability by only requiring
each agent to keep local estimates whose number grows linearly with the number
of its neighbors. We illustrate our proposed algorithm by numerical simulations
on a commodity distribution problem over a transport network.
