  This paper considers the decentralized optimization problem of minimizing a
finite sum of strongly convex and twice continuously differentiable functions
over a fixed connected undirected network. A fully decentralized primal dual
method (DPDM) is proposed. In DPDM, both primal and dual updates use second
order information while Hessian approximations are constructed by simple
algebraic calculations and at most matrix-vector products. Additionally, on
each node in the network the local direction asymptotically approaches the
centralized quasi-Newton direction. Under some mild assumptions, the proposed
algorithm is showed to have global linear convergence rate for solving strongly
convex decentralized optimization problems. Numerical results are also provided
for demonstrating the effectiveness of this new algorithm.
