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Revision of a derivative-free quasi-Newton method. (English) Zbl 0377.90085

MSC:

90C30 Nonlinear programming
90B40 Search theory
65K05 Numerical mathematical programming methods

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References:

[1] John Greenstadt, A quasi-Newton method with no derivatives, Math. Comp. 26 (1972), 145 – 166. · Zbl 0273.90053
[2] Marvin Marcus and Henryk Minc, A survey of matrix theory and matrix inequalities, Allyn and Bacon, Inc., Boston, Mass., 1964. · Zbl 0247.15002
[3] R. Fletcher and M. J. D. Powell, A rapidly convergent descent method for minimization, Comput. J. 6 (1963/1964), 163 – 168. · Zbl 0132.11603 · doi:10.1093/comjnl/6.2.163
[4] H. H. Rosenbrock, An automatic method for finding the greatest or least value of a function, Comput. J. 3 (1960/1961), 175 – 184. · doi:10.1093/comjnl/3.3.175
[5] A. R. COLVILLE, A Comparative Study of Non-Linear Programming Codes, IBM NY Scientific Center Report #320-2949, 1968. · Zbl 0224.90069
[6] M. J. D. POWELL, Comput. J., vol. 5, 1962, p. 147.
[7] R. P. BRENT, Algorithms for Finding Zeros and Extrema of Functions Without Calculating Derivatives, Stanford Univ. Comput. Sci. Report STAN-CS-71-198, 1971.
[8] R. Fletcher, Function minimization without evaluating derivatives — a review, Comput. J. 8 (1965), 33 – 41. · Zbl 0139.10401 · doi:10.1093/comjnl/8.1.33
[9] M. C. BIGGS, J. Inst. Math. Appl., vol. 8, 1972, p. 315.
[10] P. E. GILL, W. MURRAY & R. A. PITFIELD, The Implementation of Two Revised Quasi-Newton Algorithms for Unconstrained Optimization, Nat. Phys. Lab. Report NAC 11, 1972.
[11] M. J. D. POWELL, Comput. J., vol. 7, 1964, p. 155.
[12] M. J. D. Powell, A view of unconstrained minimization algorithms that do not require derivatives, ACM Trans. Math. Software 1 (1975), 97 – 107. · Zbl 0303.65059 · doi:10.1145/355637.355638
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