Citation: |
[1] |
M. Al-Baali, Descent property and global convergence of the Fletcher-Reeves method with inexact line search, IMA Journal of Numerical Analysis, 5 (1985), 121-124.doi: 10.1093/imanum/5.1.121. |
[2] |
S. Bellavia and B. Morini, A globally convergent Newton-GMRES subspace method for systems of nonlinear equations, SIAM Journal on Scientific Computing, 23 (2001), 940-960.doi: 10.1137/S1064827599363976. |
[3] |
A. Griewank, The “global” convergence of Broyden-like methods with suitable line search, Journal of Australia Mathematical Society, Ser. B, 28 (1986), 75-92. |
[4] |
W. Cheng and D. H. Li, A derivative-free nonmonotone line search and its application to the spectral residual method, IMA Journal of Numerical Analysis, 29 (2009), 814-825.doi: 10.1093/imanum/drn019. |
[5] |
Y. H. Dai and Y. Yuan, Convergence of the Fletcher-Reeves method under a generalized Wolfe search, Journal of Computational Mathematics, 2 (1996), 142-148. |
[6] |
Y. H. Dai and Y. Yuan, Convergence properties of the Fletcher-Reeves method, IMA Journal of Numerical Analysis, 16 (1996), 155-164.doi: 10.1093/imanum/16.2.155. |
[7] |
Y. H. Dai and Y. Yuan, "Nonlinear Conjugate Gradient Methods," Shanghai Science and Technology Publisher, Shanghai, 2000. |
[8] |
R. Fletcher and C. Reeves, Function minimization by conjugate gradients, Computer Journal, 7 (1964), 149-154.doi: 10.1093/comjnl/7.2.149. |
[9] |
J. C. Gilbert and J. Nocedal, Global convergence properties of conjugate gradient methods for optimization, SIAM Journal on Optimization, 2 (1992), 21-42.doi: 10.1137/0802003. |
[10] |
G. Z. Gu, D. H. Li, L. Qi and S. Z. Zhou, Descent directions of Quasi-Newton methods for symmetric nonlinear equations, SIAM Journal on Numerical Analysis, 40 (2003), 1763-1774.doi: 10.1137/S0036142901397423. |
[11] |
J. Y. Han, G. H. Liu and H. X. Yin, Convergence properties of conjugate gradient methods with strong Wolfe linesearch, Systems Science and Mathematical Science, 11 (1998), 112-116. |
[12] |
W. W. Hager and H. Zhang, A survey of nonlinear conjugate gradient methods, Pacific Journal of Optimization, 2 (2006), 35-58. |
[13] |
Y. F. Hu and C. Storey, Global convergence result for conjugate gradient methods, Journal of Optimization Theory and Applications, 71 (1991), 399-405.doi: 10.1007/BF00939927. |
[14] |
W. La Cruz and M. Raydan, Nonmonotone spectral methods for large-scale nonlinear systems, Optimization Methods and Software, 18 (2003), 583-599.doi: 10.1080/10556780310001610493. |
[15] |
W. La Cruz, J.M. Martínez and M. Raydan, Spectral resdual method without gradient information for solving large-scale nonlinear systems of equations, Mathematics of Computation, 75 (2006), 1429-1448.doi: 10.1090/S0025-5718-06-01840-0. |
[16] |
G. H. Liu, J. Y. Han and H. X. Yin, Global convergence of the Fletcher-Reeves algorithm with an inexact line search, Applied Mathematics, Journal of Chinese Universities, Ser. B, 10 (1995), 75-82. |
[17] |
D. H. Li and W. Cheng, Recent progress in the global convergence of quasi-Newton methods for nonlinear equations, Hokkaido Journal of Mathematics, 36 (2007), 729-743. |
[18] |
D. H. Li and M. Fukushima, A globally and superlinearly convergent Gauss-Newton based BFGS method for symmetric nonlinear equations, SIAM Journal on Numerical Analysis, 37 (1999), 152-172.doi: 10.1137/S0036142998335704. |
[19] |
D. H. Li and M. Fukushima, A derivative-free line search and global convergence of Broyden-like methods for nonlinear equations, Optimization Methods and Software, 13 (2000), 181-201.doi: 10.1080/10556780008805782. |
[20] |
Q. Li and D. H. Li, A class of derivative-free methods for large-scale nonlinear monotone equations, IMA Journal of Numerical Analysis, (to appear). |
[21] |
M. J. D. Powell, Some convergence properties of the conjugate gradient method, Mathematical Programming, 11 (1976), 42-49.doi: 10.1007/BF01580369. |
[22] |
M. J . D. Powell, Restart procedures of the conjugate gradient method, Mathematical Programming, 2 (1977), 241-254.doi: 10.1007/BF01593790. |
[23] |
Q. Yan, X. Z. Peng and D. H. Li, A globally convergent derivative-free method for solving large-scale nonlinear monotone equations, Journal of Computational and Applied Mathematics, 234 (2010), 649-657.doi: 10.1016/j.cam.2010.01.001. |
[24] |
J. Zhang and D. H. Li, A norm descent BFGS method for solving KKT systems of symmetric variational inequality problems, Optimization Methods and Software, 22 (2007), 237-252.doi: 10.1080/10556780500397074. |
[25] |
L. Zhang, W. Zhou and D. H. Li, Global convergence of a modified Fletcher-Reeves conjugate gradient method with Armijo-type line search, Numerische Mathematik, 104 (2006), 561-572.doi: 10.1007/s00211-006-0028-z. |
[26] |
W. Zhou and D. H. Li, Limited memory BFGS method for nonlinear monotone equations, Journal of Computational Mathematics, 25 (2007), 89-96. |
[27] |
W. Zhou and D. H. Li, A globally convergent BFGS method for nonlinear monotone equations, Mathematics of Computation, 77 (2008), 2231-2240.doi: 10.1090/S0025-5718-08-02121-2. |
[28] |
G. Zoutendijk, Nonlinear Programming, Computational Methods, in "Integer and Nonlinear Programming" (eds. J. Abadie), North-Holland, Amsterdam, (1970), 37-86. |