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Quasi-Newton Methods for Unconstrained Optimization
Abstract
A revised algorithm is given for unconstrained optimization using quasi-Newton methods. The method is based on recurring the factorization of an approximation to the Hessian matrix. Knowledge of this factorization allows greater flexibility when choosing the direction of search while minimizing the adverse effects of rounding error. The control of rounding error is particularly important when analytical derivatives are unavailable, and a modification of the algorithm to accept finite-difference approximations to the derivatives is given.
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Citations
Cited by
Representations of quasi-Newton matrices and their use in limited memory methods
Byrd, R. H., Nocedal, J., & Schnabel, R. B. (1994) · Mathematical Programming · doi:10.1007/bf01582063 · Cited by 744
Green, P. J. (1984) · Journal of the Royal Statistical Society Series B: Statistical Methodology · doi:10.1111/j.2517-6161.1984.tb01288.x · Cited by 687
Regression and ordered categorical variables
Anderson, J. A. (1984) · Journal of the Royal Statistical Society Series B: Statistical Methodology · doi:10.1111/j.2517-6161.1984.tb01270.x · Cited by 574
Large-scale linearly constrained optimization
Murtagh, B. A., & Saunders, M. A. (1978) · Mathematical Programming · doi:10.1007/bf01588950 · Cited by 527
Hybrid methods using genetic algorithms for global optimization
Renders, J.-M., & Flasse, S. P. (1996) · IEEE Transactions on Systems, Man and Cybernetics, Part B (Cybernetics) · doi:10.1109/3477.485836 · Cited by 409
Metadata
- Authors
- GILL, P. E., & MURRAY, W.
- Venue
- IMA Journal of Applied Mathematics
- Publisher
- Oxford University Press (OUP)
- Published
- 1972
- Volume
- 9
- Issue
- 1
- Pages
- 91-108
- ISSN
- 0272-4960 (ISSN-L)
- 1464-3634
- OpenAlex
- W2145126461
- Cited by
- 359
- References
- 0
- FWCI
- 7.43
- Type
- journal article
- Language
- en
- Open access
- closed
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- GILL, P. E., & MURRAY, W. (1972). Quasi-Newton Methods for Unconstrained Optimization. IMA Journal of Applied Mathematics. https://doi.org/10.1093/imamat/9.1.91
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