  We present a distributed quasi-Newton (DQN) method, which enables a group of
agents to compute an optimal solution of a separable multi-agent optimization
problem locally using an approximation of the curvature of the aggregate
objective function. Each agent computes a descent direction from its local
estimate of the aggregate Hessian, obtained from quasi-Newton approximation
schemes using the gradient of its local objective function. Moreover, we
introduce a distributed quasi-Newton method for equality-constrained
optimization (EC-DQN), where each agent takes Karush-Kuhn-Tucker-like update
steps to compute an optimal solution. In our algorithms, each agent
communicates with its one-hop neighbors over a peer-to-peer communication
network to compute a common solution. We prove convergence of our algorithms to
a stationary point of the optimization problem. In addition, we demonstrate the
competitive empirical convergence of our algorithm in both well-conditioned and
ill-conditioned optimization problems, in terms of the computation time and
communication cost incurred by each agent for convergence, compared to existing
distributed first-order and second-order methods. Particularly, in
ill-conditioned problems, our algorithms achieve a faster computation time for
convergence, while requiring a lower communication cost, across a range of
communication networks with different degrees of connectedness, by leveraging
information on the curvature of the problem.
