OASIcs.ATMOS.2023.3.pdf
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Convergence Properties of Newton’s Method for Globally Optimal Free Flight Trajectory Optimization (Short Paper)
Authors
Ralf Borndörfer 
,
Fabian Danecker ,
Martin Weiser
-
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Volume:
23rd Symposium on Algorithmic Approaches for Transportation Modelling, Optimization, and Systems (ATMOS 2023)
Series: Open Access Series in Informatics (OASIcs)
Conference: Symposium on Algorithmic Approaches for Transportation Modelling, Optimization, and Systems (ATMOS) - License:
Creative Commons Attribution 4.0 International license
- Publication Date: 2023-08-31
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Ralf Borndörfer, Fabian Danecker, and Martin Weiser. Convergence Properties of Newton’s Method for Globally Optimal Free Flight Trajectory Optimization (Short Paper). In 23rd Symposium on Algorithmic Approaches for Transportation Modelling, Optimization, and Systems (ATMOS 2023). Open Access Series in Informatics (OASIcs), Volume 115, pp. 3:1-3:6, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2023)
https://doi.org/10.4230/OASIcs.ATMOS.2023.3
https://doi.org/10.4230/OASIcs.ATMOS.2023.3
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.
Subject Classification
ACM Subject Classification
- Mathematics of computing → Continuous functions
- Mathematics of computing → Continuous optimization
- Mathematics of computing → Discretization
- Mathematics of computing → Discrete optimization
- Mathematics of computing → Network optimization
- Mathematics of computing → Graph algorithms
- Mathematics of computing → Nonconvex optimization
- Mathematics of computing → Ordinary differential equations
Keywords
- shortest path
- flight planning
- free flight
- optimal control
- global optimization
- Newton’s method
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References
- R. Borndörfer, F. Danecker, and M. Weiser. A Discrete-Continuous Algorithm for Free Flight Planning. Algorithms, 14(1):4, 2021. URL: https://doi.org/10.3390/a14010004.
- R. Borndörfer, F. Danecker, and M. Weiser. A Discrete-Continuous Algorithm for Globally Optimal Free Flight Trajectory Optimization. In 22nd Symposium on Algorithmic Approaches for Transportation Modelling, Optimization, and Systems (ATMOS 2022), 2022. URL: https://doi.org/10.4230/OASIcs.ATMOS.2022.2.
- R. Borndörfer, F. Danecker, and M. Weiser. Error Bounds for Discrete-Continuous Free Flight Trajectory Optimization. Journal of Optimization Theory and Applications, July 2023. URL: https://doi.org/10.1007/s10957-023-02264-7.
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