Newton's Method for Global Free Flight Trajectory Optimization

TL;DR

This paper demonstrates that Newton's method can reliably converge for global free flight trajectory optimization under certain conditions, enabling more effective combined discrete and continuous optimization approaches.

Contribution

It provides theoretical proof that Newton's method converges locally for free flight trajectory optimization, supporting its use in global optimization frameworks.

Findings

Newton's method converges under specific assumptions.

Supports combined discrete and continuous optimization.

Enhances reliability of trajectory optimization methods.

Abstract

Globally optimal free flight trajectory optimization can be achieved with a combination of discrete and continuous optimization. A key requirement is that Newton's method for continuous optimization converges in a sufficiently large neighborhood around a minimizer. We show in this paper that, under certain assumptions, this is the case.