  We consider a class of distributed optimization problem where the objective
function consists of a sum of strongly convex and smooth functions and a
(possibly nonsmooth) convex regularizer. A multi-agent network is assumed,
where each agent holds a private cost function and cooperates with its
neighbors to compute the optimum of the aggregate objective. We propose a
quasi-Newton Alternating Direction Method of Multipliers (ADMM) where the
primal update is solved inexactly with approximated curvature information. By
introducing an intermediate consensus variable, we achieve a block diagonal
Hessian which eliminates the need for inner communication loops within the
network when computing the update direction. We establish global linear
convergence to the optimal primal-dual solution without the need for
backtracking line search, under the assumption that component cost functions
are strongly convex with Lipschitz continuous gradients. Numerical simulations
on real datasets demonstrate the advantages of the proposed method over state
of the art.
