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References
E.M.L. Beale (1972). A derivation of conjugate gradients, in F.A. Lootsma, ed., Numerical Methods for Nonlinear Optimization, pp. 39–43, Academic Press.
A.G. Buckley (1978). A combined conjugate-gradient quasi-Newton minimization algorithm, Math. Programming 15, 200–210.
A.G. Buckely (1984). Termination and equivalence results for conjugate gradient algorithms, Math. Programming 29, No. 1, 67–76.
W.C. Davidon (1980). Conic approximations and collinear scalings for optimizers, SIAM J. Num. Anal. 17, 268–281.
W.C. Davidon (1982). Conjugate directions for conic functions, in M.J.D. Powell, ed., Nonlinear Optimization 1981, Academic Press.
J.E. Dennis and R. Schnabel (1983). Numerical Methods for Unconstrained Optimization and Nonlinear Equations, Prentice Hall.
R. Fletcher and C. Reeves (1964). Function minimization by conjugate gradients, The Computer Journal 7, 149–154.
R. Fletcher (1970). A new approach to variable metric algorithms, Computer J. 13, 317–322.
P. Gill, W. Murray and M. Wright (1981). Practical Optimization, Academic Press.
H. Gourgeon and J. Nocedal (1985). A conic algorithm for Optimization, SIAM J. on Scientific and Statistical Computing 6, No. 2, 253–267.
M.D. Hebden (1973). An algorithm for minimization using exact second derivatives, Rept TP515, A.E.R.E., Harwell.
J.J. Morè (1977). The Levenberg-Marquardt algorithm: Implementation and theory, in G.A. Watson, ed., Numerical Analysis, Lecture Notes in Math. 630, Springer Verlag, 105–116.
J.J. Morè (1982). Recent developments in algorithms and software for trust region methods, ANL/MCS-TM-2, Argonne National Laboratory.
L. Nazareth and J. Nocedal (1982). Conjugate gradient methods with variable storage, Math. Programming 23, 326–340.
J. Nocedal (1980). Updating quasi-Newton matrices with limited storage, Math. Comp. 35, 773–782.
M.J.D. Powell (1977). Restart procedures for the conjugate gradient method, Math. Programming 12, 241–254.
D.F. Shanno (1978). Conjugate gradient methods with inexact line searches, Mathematics of Operations Research 3, 244–256.
D.F. Shanno and K. Phua (1978). A variable method subroutine for unconstrained nonlinear optimization, MIS tech. Rep. 28, University of Arizona.
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Nocedal, J. (1986). Viewing the conjugate gradient method as a trust region algorithm. In: Hennart, JP. (eds) Numerical Analysis. Lecture Notes in Mathematics, vol 1230. Springer, Berlin, Heidelberg. https://doi.org/10.1007/BFb0072675
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DOI: https://doi.org/10.1007/BFb0072675
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