Hessians in Birkhoff-Theoretic Trajectory Optimization
Optimization and Control
2025-11-19 v1 Mathematical Software
Numerical Analysis
Robotics
Numerical Analysis
Abstract
This paper derives various Hessians associated with Birkhoff-theoretic methods for trajectory optimization. According to a theorem proved in this paper, approximately 80% of the eigenvalues are contained in the narrow interval [-2, 4] for all Birkhoff-discretized optimal control problems. A preliminary analysis of computational complexity is also presented with further discussions on the grand challenge of solving a million point trajectory optimization problem.
Cite
@article{arxiv.2511.13963,
title = {Hessians in Birkhoff-Theoretic Trajectory Optimization},
author = {I. M. Ross},
journal= {arXiv preprint arXiv:2511.13963},
year = {2025}
}
Comments
This paper appeared as an Engineering Note in the J. Guid. Control & Dynamics