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29 juillet 2022
- 2208.00057
- Computational Optimization and Applications 80:55-88 (2021)
- doi: 10.1007/s10589-021-00297-0
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Mathematics - Optimization and Control Computer Science - Mathematical Software Economics - Econometrics Mathematics - Numerical Analysis Statistics - Computation 90C06, 90C53, 65K10,Sujets proches
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Johannes J. Brust et al., « Compact representations of structured BFGS matrices », arXiv - économie, ID : 10.1007/s10589-021-00297-0
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Résumé
For general large-scale optimization problems compact representations exist in which recursive quasi-Newton update formulas are represented as compact matrix factorizations. For problems in which the objective function contains additional structure, so-called structured quasi-Newton methods exploit available second-derivative information and approximate unavailable second derivatives. This article develops the compact representations of two structured Broyden-Fletcher-Goldfarb-Shanno update formulas. The compact representations enable efficient limited memory and initialization strategies. Two limited memory line search algorithms are described and tested on a collection of problems, including a real world large scale imaging application.