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Conditioning of quasi-Newton methods for function minimization. (English) Zbl 0225.65073


MSC:

90C30 Nonlinear programming
65K05 Numerical mathematical programming methods
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[1] R. Fletcher and M. J. D. Powell, A rapidly convergent descent method for minimization, Comput. J. 6 (1963/1964), 163 – 168. · Zbl 0132.11603
[2] W. C. Davidon, Variable Metric Method for Minimization, Argonne National Laboratory Report ANL-5990, November 1959.
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[5] E. M. Rosen, ”A review of quasi-Newton methods in nonlinear equation solving and unconstrained optimization,” Nat. Conference of the ACM, Proceedings of the Twenty-First Conference, Thompson Book Co., Washington, D.C., 1966, pp. 37-41.
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[7] M. J. Box, A comparison of several current optimization methods, and the use of transformations in constrained problems, Comput. J. 9 (1966), 67 – 77. · Zbl 0146.13304
[8] A. Leon, A Comparison Among Eight Known Optimizing Procedures, Internal Working Paper No. 20, Space Sciences Laboratory, University of California, Berkeley, August 1964.
[9] J. D. Pearson, On Variable Metric Methods of Minimization, Research Analysis Corp. Technical Paper, RAC-TP-302, February 1968.
[10] C. G. Broyden, Quasi-Newton methods and their application to function minimisation, Math. Comp. 21 (1967), 368 – 381. · Zbl 0155.46704
[11] Donald Goldfarb, A family of variable-metric methods derived by variational means, Math. Comp. 24 (1970), 23 – 26. · Zbl 0196.18002
[12] D. F. Shanno and P. C. Kettler, Optimal conditioning of quasi-Newton methods, Math. Comp. 24 (1970), 657 – 664. · Zbl 0225.65074
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