# Weight Design of Distributed Approximate Newton Algorithms for Constrained Optimization

## TL;DR

This paper introduces a distributed approximate Newton algorithm for constrained optimization that requires minimal communication, with a novel weight design that enhances convergence compared to first-order methods.

## Contribution

It proposes a new distributed approximate Newton algorithm with an innovative weight design for improved convergence in constrained optimization.

## Key findings

- The algorithm only requires constant-size communication messages.
- The proposed weight design improves convergence over existing methods.
- Simulations confirm superior performance of the new approach.

## 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.