Weight Design of Distributed Approximate Newton Algorithms for Constrained Optimization

Abstract: 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.