A Primal-Dual Quasi-Newton Method for Consensus Optimization

We introduce the primal-dual quasi-Newton (PDQN) method as an approximated second order method for solving decentralized optimization problems. The PD-QN method performs quasi-Newton, or approximate second order, updates on both the primal and dual variables of the consensus optimization problem. The quasi-Newton updates remove the internal minimization step necessary in most dual methods and also make the method more robust in ill-conditioned settings relative to first order methods. The linear convergence rate of PD-QN is established formally and strong performance advantages relative to existing dual and primal-dual methods are shown numerically.