A Distributed Continuous-time Modified Newton-Raphson Algorithm

TL;DR

This paper introduces a continuous-time second-order optimization algorithm suitable for distributed implementation, achieving convergence rates comparable to Newton-Raphson and demonstrated through theoretical analysis and numerical examples.

Contribution

It presents a novel distributed continuous-time second-order optimization algorithm with proven convergence, enhancing efficiency over traditional methods.

Findings

Comparable convergence rate to Newton-Raphson method

Distributed implementation with proven convergence

Numerical example validating the approach

Abstract

We propose a continuous-time second-order optimization algorithm for solving unconstrained convex optimization problems with bounded Hessian. We show that this alternative algorithm has a comparable convergence rate to that of the continuous-time Newton-Raphson method, however structurally, it is amenable to a more efficient distributed implementation. We present a distributed implementation of our proposed optimization algorithm and prove its convergence via Lyapunov analysis. A numerical example demonstrates our results.