Convergence Properties of Newton's Method for Globally Optimal Free Flight Trajectory Optimization
Please always quote using this URN: urn:nbn:de:0297-zib-91309
- 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.
Download full text files
Additional Services
| Author: | Ralf BorndörferORCiD, Fabian DaneckerORCiD, Martin WeiserORCiD |
|---|---|
| Document Type: | ZIB-Report |
| Tag: | Newton's method; flight planning; free flight; global optimization; optimal control; shortest path |
| MSC-Classification: | 49-XX CALCULUS OF VARIATIONS AND OPTIMAL CONTROL; OPTIMIZATION [See also 34H05, 34K35, 65Kxx, 90Cxx, 93-XX] |
| 65-XX NUMERICAL ANALYSIS | |
| 90-XX OPERATIONS RESEARCH, MATHEMATICAL PROGRAMMING | |
| CCS-Classification: | G. Mathematics of Computing / G.1 NUMERICAL ANALYSIS / G.1.6 Optimization / Global optimization (NEW) |
| G. Mathematics of Computing / G.1 NUMERICAL ANALYSIS / G.1.7 Ordinary Differential Equations / Boundary value problems | |
| G. Mathematics of Computing / G.2 DISCRETE MATHEMATICS / G.2.2 Graph Theory (F.2.2) / Graph algorithms | |
| Date of first Publication: | 2023/07/06 |
| Series (Serial Number): | ZIB-Report (23-19) |
| ISSN: | 1438-0064 |
