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On the rate of superlinear convergence of a class of variable metric methods. (English) Zbl 0459.65043


MSC:

65K05 Numerical mathematical programming methods
90C30 Nonlinear programming
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References:

[1] Broyden, C.G.: Quasi-Newton methods and their application to function minimization. Math. Comput.21, 368-381 (1967) · Zbl 0155.46704 · doi:10.1090/S0025-5718-1967-0224273-2
[2] Broyden, C.G.: The convergence of a class of double-rank minimization algorithms, Parts 1 and 2. J. Inst. Math. Appl.6, 76-90, 222-231 (1970) · Zbl 0223.65023 · doi:10.1093/imamat/6.1.76
[3] Burmeister, W.: Die Konvergenzordnung des Fletcher-Powell-Algorithmus. Z. Angew. Math. Mech.53, 693-699 (1973) · Zbl 0269.90039 · doi:10.1002/zamm.19730531007
[4] Davidon, W.C.: Variable metric methods for minimization. Argonne National Laboratories rept. ANL-5990 (1959)
[5] Dixon, L.C.W.: Variable metric algorithms: necessary and sufficient conditions for identical behaviour on non-quadratic functions. J. Optimization Theory Appl.10, 34-40 (1972) · Zbl 0226.49014 · doi:10.1007/BF00934961
[6] Fletcher, R.: A new approach to variable metric algorithms. Comput. J.13, 317-322 (1970) · Zbl 0207.17402 · doi:10.1093/comjnl/13.3.317
[7] Fletcher, R., Powell, M.J.D.: A rapidly convergent descent method for minimization. Comput. J.6, 163-168 (1963) · Zbl 0132.11603
[8] Goldfarb, D.: A family of variable metric methods derived by variational means. Math. Comput.24, 23-26 (1970) · Zbl 0196.18002 · doi:10.1090/S0025-5718-1970-0258249-6
[9] Huang, H.Y.: Unified approach to quadratically convergent algorithms for function minimization. J. Optimization Theory Appl.5, 405-423 (1970) · Zbl 0194.19402 · doi:10.1007/BF00927440
[10] Noble, B.: Applied linear algebra. New York: Prentice-Hall, 1969 · Zbl 0203.33201
[11] Ritter, K.: Global and superlinear convergence of a class of variable metric methods. Mathematics Research Center TSR # 1945, University of Wisconsin-Madison 1979
[12] Schuller, G.: On the order of convergence of certain quasi-Newton Methods. Numer. Math.23, 181-192 (1974) · Zbl 0292.65034 · doi:10.1007/BF01459951
[13] Shanno, D.F.: conditioning of quasi-Newton methods for function minimization. Math. Comput.24, 647-656 (1970) · Zbl 0225.65073 · doi:10.1090/S0025-5718-1970-0274029-X
[14] Stoer, J.: On the convergence rate of imperfect minimization algorithms in Broyden.s ?-class. Math. Programming9, 313-335 (1975) · Zbl 0346.90047 · doi:10.1007/BF01681353
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