  This paper considers an optimization problem that components of the objective
function are available at different nodes of a network and nodes are allowed to
only exchange information with their neighbors. The decentralized alternating
method of multipliers (DADMM) is a well-established iterative method for
solving this category of problems; however, implementation of DADMM requires
solving an optimization subproblem at each iteration for each node. This
procedure is often computationally costly for the nodes. We introduce a
decentralized quadratic approximation of ADMM (DQM) that reduces computational
complexity of DADMM by minimizing a quadratic approximation of the objective
function. Notwithstanding that DQM successively minimizes approximations of the
cost, it converges to the optimal arguments at a linear rate which is identical
to the convergence rate of DADMM. Further, we show that as time passes the
coefficient of linear convergence for DQM approaches the one for DADMM.
Numerical results demonstrate the effectiveness of DQM.
