Convergence Properties of Newton's Method for Globally Optimal Free Flight Trajectory Optimization

TL;DR

This paper investigates the convergence behavior of Newton's method in free flight trajectory optimization, revealing larger practical convergence domains and proposing domain decomposition to enhance performance.

Contribution

It provides numerical evidence that the actual convergence radius exceeds theoretical bounds and introduces a domain decomposition technique to improve convergence.

Findings

Practical convergence radius is larger than theoretical bounds

Domain decomposition improves convergence efficiency

Numerical evidence supports enhanced convergence properties

Abstract

The algorithmic efficiency of Newton-based methods for Free Flight Trajectory Optimization is heavily influenced by the size of the domain of convergence. We provide numerical evidence that the convergence radius is much larger in practice than what the theoretical worst case bounds suggest. The algorithm can be further improved by a convergence-enhancing domain decomposition.