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References:
[1] M. Al-Bali: Descent property and global convergence of the Fletcher-Reeves method with inexact line search. IMA J. Numer. Anal. 5 (1985), 121-124. MR 0777963
[2] P. Baptist, J. Stoer: On the relation between quadratic termination and convergence properties of minimization algorithms. Part 2. Applications. Numer. Math. 28 (1977), 367-391. MR 0496671 | Zbl 0366.65028
[3] P. Bjorstadt, J. Nocedal: Analysis of a new algorithm for one-dimensional minimization. Computing 22 (1979), 93-100. MR 0620386
[4] A. R. Conn N. I. M. Gould, P. L. Toint: Testing a class of methods for solving minimization problems with simple bounds on the variables. Math. Comp. 50 (1988), 399-430. MR 0929544
[5] W.C. Davidon: Variable metric method for minimization. A.E.C. Research and Development Report ANL-5990, 1959.
[6] W.C. Davidon: Optimally conditioned optimization algorithms without line searches. Math. Pro- gramming 9 (1975), 1-30. MR 0383741 | Zbl 0328.90055
[7] R. S. Dembo, T. Steihaug: Truncated-Newton algorithms for large-scale unconstrained minimization. Math. Programming 26 (1983), 190-212. MR 0700647
[8] R. Fletcher: A FORTRAN subroutine for minimization by the method of conjugate gradients. Report No. AERE-R7073, Atomic Energy Research Establishment, Harwell 1972.
[9] R. Fletcher, M.J. D. Powell: A rapidly convergent descent method for minimization. Computer J. 6 (1963), 163-168. MR 0152116 | Zbl 0132.11603
[10] R. Fletcher, CM. Reeves: Function minimization by conjugate gradients. Computer J. 7 (1964), 149-154. MR 0187375 | Zbl 0132.11701
[11] J.C. Gilbert, and J. Nocedal: Global convergence properties of conjugate gradient methods for optimization. Report No. 1268, Institut National de Recherche en Inforrnatique et. en Automatique, 1990.
[12] A. Griewank, P. L. Toint: Partitioned variable metric updates for large structured optimization problems. Numer. Math. 39 (1982), 119-137. MR 0664541 | Zbl 0482.65035
[13] M. R. Hestenes, CM. Stiefel: Methods of conjugate gradient for solving linear systems. J. Res. Nat. Bur. Standards 49 (1964), 409-436. MR 0060307
[14] Y. F. Hu, C. Storey: A Global Convergence Result for Conjugate Gradient Methods. Report No. A134, Loughborough University of Technology, 1990. MR 1131466
[15] K.M. Khoda Y. Liu, C. Storey: A Generalized Polak-Ribiére Algorithm. Report No. A128, Loughborough University of Technology, 1990.
[16] L. Lukšan: Variable Metric Methods. Unconstrained Minimization. Academia, Prague 1990. In Czech. MR 1147645
[17] L. Lukšan: Computational experience with improved variable metric methods for unconstrained minimization. Kybernetika 26 (1990), 415-431. MR 1079679
[18] J.J. Moré B.S. Garbow, K.E. Hillstrom: Testing unconstrained optimization software. ACM Trans. Math. Software 7 (1981), 17-41. MR 0607350
[19] J. Nocedal: Updating quasi-Newton matrices with limited storage. Math. Comp. 35 (1980), 773-782. MR 0572855 | Zbl 0464.65037
[20] E. Polak, G. Ribiére: Note sur la convergence de methodes de directions conjugees. Revue Francaise Inform. Mech. Oper. 16-R1 (1969), 35-43. MR 0255025
[21] M.J.D. Powell: Restart procedures of the conjugate gradient method. Math. Programming 12 (1977), 241-254. MR 0478622
[22] M.J.D. Powell: Nonconvex Minimization Calculations and the Conjugate Gradient Method. Report No. DAMTP 1983/NA14, University of Cambridge, 1983. MR 0760460
[23] M.J.D. Powell: Convergence Properties of Algorithms for Nonlinear Optimization. Report No. DAMPT 1985/NA1, University of Cambridge, 1985. MR 0867680
[24] D. F. Shanno: Conditioning of quasi-Newton methods for function minimization. Math. Comp. 24 (1970), 647-656. MR 0274029
[25] D.F. Shanno: Globally convergent conjugate gradient algorithms. Math. Programming 33 (1985), 61-67. MR 0809749 | Zbl 0579.90079
[26] P. L. Toint: On sparse and symmetric matrix updating subject to a linear equation. Math. Comp. 31 (1987), 954-961. MR 0455338
[27] D. Touati-Ahmed, C. Storey: Efficient hybrid conjugate gradient techniques. J. Optim. Theory Appl. 64 (1990), 379-397. MR 1042002 | Zbl 0666.90063
[28] G. Zoutendijk: Nonlinear programming, computational methods. In: Integer and Nonlinear Programming (J. Abadie, ed.), North-Holland, Amsterdam 1970, pp. 93-121. MR 0437081 | Zbl 0336.90057
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