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.
Convergence Properties of Newton’s Method for Globally Optimal Free Flight Trajectory Optimization (Short Paper)
2023-08-31
6 pages , 711996 byte
OASIcs, Vol. 115, 23rd Symposium on Algorithmic Approaches for Transportation Modelling, Optimization, and Systems (ATMOS 2023), pages 3:1-3:6
Conference paper
Electronic Resource
English
Mathematics of computing → Network optimization , global optimization , Mathematics of computing → Continuous optimization , optimal control , Mathematics of computing → Discrete optimization , Mathematics of computing → Ordinary differential equations , Mathematics of computing → Continuous functions , Mathematics of computing → Discretization , free flight , Newton’s method , flight planning , Mathematics of computing → Nonconvex optimization , shortest path , Mathematics of computing → Graph algorithms
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