Global optimization (NEW)
Refine
Document Type
- ZIB-Report (2)
Language
- English (2)
Has Fulltext
- yes (2)
Is part of the Bibliography
- no (2)
Keywords
- global optimization (2)
- Newton's method (1)
- bivariate functions (1)
- convex envelope (1)
- flight planning (1)
- free flight (1)
- linear underestimator (1)
- optimal control (1)
- shortest path (1)
Convergence Properties of Newton's Method for Globally Optimal Free Flight Trajectory Optimization
(2023)
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.
This is a technical report for the SCIP constraint handler cons_bivariate. We describe a cut-generation algorithm for a class of bivariate twice continuously differentiable functions with
fixed convexity behavior over a box.
Computational results comparing our cut-generation algorithms with
state-of-the-art global
optimization software on a series of randomly generated test instances are reported and discussed.