  Motivated by economic dispatch and linearly-constrained resource allocation
problems, this paper proposes a novel Distributed Approx-Newton algorithm that
approximates the standard Newton optimization method. A main property of this
distributed algorithm is that it only requires agents to exchange constant-size
communication messages. The convergence of this algorithm is discussed and
rigorously analyzed. In addition, we aim to address the problem of designing
communication topologies and weightings that are optimal for second-order
methods. To this end, we propose an effective approximation which is loosely
based on completing the square to address the NP-hard bilinear optimization
involved in the design. Simulations demonstrate that our proposed weight design
applied to the Distributed Approx-Newton algorithm has a superior convergence
property compared to existing weighted and distributed first-order gradient
descent methods.
