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Nonlinear conjugate gradient methods with sufficient descent properties for unconstrained optimization
1. | Central Japan Railway Company, JR Central Towers, 1-1-4, Meieki, Nakamura-ku, Nagoya, Aichi 450-6101, Japan |
2. | Department of Management System Science, Yokohama National University, 79-4 Tokiwadai, Hodogaya-ku, Yokohama 240-8501, Japan |
3. | Department of Mathematical Information Science, Tokyo University of Science, 1-3, Kagurazaka, Shinjuku-ku, Tokyo 162-8601, Japan |
References:
[1] |
N. Andrei, A Dai-Yuan conjugate gradient algorithm with sufficient descent and conjugacy conditions for unconstrained optimization,, Applied Mathematics Letters, 21 (2008), 165.
doi: 10.1016/j.aml.2007.05.002. |
[2] |
N. Andrei, New accelerated conjugate gradient algorithms as a modification of Dai-Yuan's computational scheme for unconstrained optimization,, Journal of Computational and Applied Mathematics, 234 (2010), 3397.
doi: 10.1016/j.cam.2010.05.002. |
[3] |
I. Bongartz, A. R. Conn, N. I. M. Gould and P. L. Toint, CUTE: Constrained and unconstrained testing environments,, ACM Transactions on Mathematical Software, 21 (1995), 123.
doi: 10.1145/200979.201043. |
[4] |
X. Chen and J. Sun, Global convergence of a two-parameter family of conjugate gradient methods without line search,, Journal of Computational and Applied Mathematics, 146 (2002), 37.
doi: 10.1016/S0377-0427(02)00416-8. |
[5] |
W. Cheng, A two-term PRP-based descent method,, Numerical Functional Analysis and Optimization, 28 (2007), 1217.
doi: 10.1080/01630560701749524. |
[6] |
Y. H. Dai, Nonlinear conjugate gradient methods,, in, (2011).
doi: 10.1002/9780470400531.eorms0183. |
[7] |
Y. H. Dai and L. Z. Liao, New conjugacy conditions and related nonlinear conjugate gradient methods,, Applied Mathematics and Optimization, 43 (2001), 87.
doi: 10.1007/s002450010019. |
[8] |
Y. H. Dai and Y. Yuan, A nonlinear conjugate gradient method with a strong global convergence property,, SIAM Journal on Optimization, 10 (1999), 177.
doi: 10.1137/S1052623497318992. |
[9] |
Y. H. Dai and Y. Yuan, A three-parameter family of nonlinear conjugate gradient methods,, Mathematics of Computation, 70 (2001), 1155.
doi: 10.1090/S0025-5718-00-01253-9. |
[10] |
Z. Dai and B. S. Tian, Global convergence of some modified PRP nonlinear conjugate gradient methods,, Optimization Letters, 5 (2011), 615.
doi: 10.1007/s11590-010-0224-8. |
[11] |
Z. Dai and F. Wen, A modified CG-DESCENT method for unconstrained optimization,, Journal of Computational and Applied Mathematics, 235 (2011), 3332.
doi: 10.1016/j.cam.2011.01.046. |
[12] |
E. D. Dolan and J. J. Moré, Benchmarking optimization software with performance profiles,, Mathematical Programming, 91 (2002), 201.
doi: 10.1007/s101070100263. |
[13] |
R. Fletcher, "Practical Methods of Optimization,", $2^{nd}$ edition, (1987).
|
[14] |
R. Fletcher and C. M. Reeves, Function minimization by conjugate gradients,, The Computer Journal, 7 (1964), 149.
doi: 10.1093/comjnl/7.2.149. |
[15] |
N. I. M. Gould, D. Orban and P. L. Toint, CUTEr and SifDec: A constrained and unconstrained testing environment, revisited,, ACM Transactions on Mathematical Software, 29 (2003), 373.
doi: 10.1145/962437.962439. |
[16] |
W. W. Hager and H. Zhang, A new conjugate gradient method with guaranteed descent and an efficient line search,, SIAM Journal on Optimization, 16 (2005), 170.
doi: 10.1137/030601880. |
[17] |
W. W. Hager and H. Zhang, A survey of nonlinear conjugate gradient methods,, Pacific Journal of Optimization, 2 (2006), 35.
|
[18] |
W. W. Hager and H. Zhang, "CG_DESCENT Version 1.4, User's Guide,", University of Florida, (2005). Google Scholar |
[19] |
M. R. Hestenes and E. Stiefel, Methods of conjugate gradients for solving linear systems,, Journal of Research of the National Bureau of Standards, 49 (1952), 409.
doi: 10.6028/jres.049.044. |
[20] |
M. Li and H. Feng, A sufficient descent LS conjugate gradient method for unconstrained optimization problems,, Applied Mathematics and Computation, 218 (2011), 1577.
doi: 10.1016/j.amc.2011.06.034. |
[21] |
Y. Liu and C. Storey, Efficient generalized conjugate gradient algorithms, part 1: Theory,, Journal of Optimization Theory and Applications, 69 (1991), 129.
doi: 10.1007/BF00940464. |
[22] |
Y. Narushima and H. Yabe, Conjugate gradient methods based on secant conditions that generate descent search directions for unconstrained optimization,, Journal of Computational and Applied Mathematics, 236 (2012), 4303.
doi: 10.1016/j.cam.2012.01.036. |
[23] |
Y. Narushima, H. Yabe and J. A. Ford, A three-term conjugate gradient method with sufficient descent property for unconstrained optimization,, SIAM Journal on Optimization, 21 (2011), 212.
doi: 10.1137/080743573. |
[24] |
J. Nocedal and S. J. Wright, "Numerical Optimization,", $2^{nd}$ edition, (2006).
|
[25] |
K. Sugiki, Y. Narushima and H. Yabe, Globally convergent three-term conjugate gradient methods that use secant conditions and generate descent search directions for unconstrained optimization,, Journal of Optimization Theory and Applications, 153 (2012), 733.
doi: 10.1007/s10957-011-9960-x. |
[26] |
W. Sun and Y. Yuan, "Optimization Theory and Methods: Nonlinear Programming,", Springer, (2006).
|
[27] |
G. Yu, L. Guan and W. Chen, Spectral conjugate gradient methods with sufficient descent property for large-scale unconstrained optimization,, Optimization Methods and Software, 23 (2008), 275.
doi: 10.1080/10556780701661344. |
[28] |
G. Yu, L. Guan and G. Li, Global convergence of modified Polak-Ribière-Polyak conjugate gradient methods with sufficient descent property,, Journal of Industrial and Management Optimization, 4 (2008), 565.
doi: 10.3934/jimo.2008.4.565. |
[29] |
G. Yuan, Modified nonlinear conjugate gradient methods with sufficient descent property for large-scale optimization problems,, Optimization Letters, 3 (2009), 11.
doi: 10.1007/s11590-008-0086-5. |
[30] |
L. Zhang and J. Li, A new globalization technique for nonlinear conjugate gradient methods for nonconvex minimization,, Applied Mathematics and Computation, 217 (2011), 10295.
doi: 10.1016/j.amc.2011.05.032. |
[31] |
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.
doi: 10.1007/s00211-006-0028-z. |
show all references
References:
[1] |
N. Andrei, A Dai-Yuan conjugate gradient algorithm with sufficient descent and conjugacy conditions for unconstrained optimization,, Applied Mathematics Letters, 21 (2008), 165.
doi: 10.1016/j.aml.2007.05.002. |
[2] |
N. Andrei, New accelerated conjugate gradient algorithms as a modification of Dai-Yuan's computational scheme for unconstrained optimization,, Journal of Computational and Applied Mathematics, 234 (2010), 3397.
doi: 10.1016/j.cam.2010.05.002. |
[3] |
I. Bongartz, A. R. Conn, N. I. M. Gould and P. L. Toint, CUTE: Constrained and unconstrained testing environments,, ACM Transactions on Mathematical Software, 21 (1995), 123.
doi: 10.1145/200979.201043. |
[4] |
X. Chen and J. Sun, Global convergence of a two-parameter family of conjugate gradient methods without line search,, Journal of Computational and Applied Mathematics, 146 (2002), 37.
doi: 10.1016/S0377-0427(02)00416-8. |
[5] |
W. Cheng, A two-term PRP-based descent method,, Numerical Functional Analysis and Optimization, 28 (2007), 1217.
doi: 10.1080/01630560701749524. |
[6] |
Y. H. Dai, Nonlinear conjugate gradient methods,, in, (2011).
doi: 10.1002/9780470400531.eorms0183. |
[7] |
Y. H. Dai and L. Z. Liao, New conjugacy conditions and related nonlinear conjugate gradient methods,, Applied Mathematics and Optimization, 43 (2001), 87.
doi: 10.1007/s002450010019. |
[8] |
Y. H. Dai and Y. Yuan, A nonlinear conjugate gradient method with a strong global convergence property,, SIAM Journal on Optimization, 10 (1999), 177.
doi: 10.1137/S1052623497318992. |
[9] |
Y. H. Dai and Y. Yuan, A three-parameter family of nonlinear conjugate gradient methods,, Mathematics of Computation, 70 (2001), 1155.
doi: 10.1090/S0025-5718-00-01253-9. |
[10] |
Z. Dai and B. S. Tian, Global convergence of some modified PRP nonlinear conjugate gradient methods,, Optimization Letters, 5 (2011), 615.
doi: 10.1007/s11590-010-0224-8. |
[11] |
Z. Dai and F. Wen, A modified CG-DESCENT method for unconstrained optimization,, Journal of Computational and Applied Mathematics, 235 (2011), 3332.
doi: 10.1016/j.cam.2011.01.046. |
[12] |
E. D. Dolan and J. J. Moré, Benchmarking optimization software with performance profiles,, Mathematical Programming, 91 (2002), 201.
doi: 10.1007/s101070100263. |
[13] |
R. Fletcher, "Practical Methods of Optimization,", $2^{nd}$ edition, (1987).
|
[14] |
R. Fletcher and C. M. Reeves, Function minimization by conjugate gradients,, The Computer Journal, 7 (1964), 149.
doi: 10.1093/comjnl/7.2.149. |
[15] |
N. I. M. Gould, D. Orban and P. L. Toint, CUTEr and SifDec: A constrained and unconstrained testing environment, revisited,, ACM Transactions on Mathematical Software, 29 (2003), 373.
doi: 10.1145/962437.962439. |
[16] |
W. W. Hager and H. Zhang, A new conjugate gradient method with guaranteed descent and an efficient line search,, SIAM Journal on Optimization, 16 (2005), 170.
doi: 10.1137/030601880. |
[17] |
W. W. Hager and H. Zhang, A survey of nonlinear conjugate gradient methods,, Pacific Journal of Optimization, 2 (2006), 35.
|
[18] |
W. W. Hager and H. Zhang, "CG_DESCENT Version 1.4, User's Guide,", University of Florida, (2005). Google Scholar |
[19] |
M. R. Hestenes and E. Stiefel, Methods of conjugate gradients for solving linear systems,, Journal of Research of the National Bureau of Standards, 49 (1952), 409.
doi: 10.6028/jres.049.044. |
[20] |
M. Li and H. Feng, A sufficient descent LS conjugate gradient method for unconstrained optimization problems,, Applied Mathematics and Computation, 218 (2011), 1577.
doi: 10.1016/j.amc.2011.06.034. |
[21] |
Y. Liu and C. Storey, Efficient generalized conjugate gradient algorithms, part 1: Theory,, Journal of Optimization Theory and Applications, 69 (1991), 129.
doi: 10.1007/BF00940464. |
[22] |
Y. Narushima and H. Yabe, Conjugate gradient methods based on secant conditions that generate descent search directions for unconstrained optimization,, Journal of Computational and Applied Mathematics, 236 (2012), 4303.
doi: 10.1016/j.cam.2012.01.036. |
[23] |
Y. Narushima, H. Yabe and J. A. Ford, A three-term conjugate gradient method with sufficient descent property for unconstrained optimization,, SIAM Journal on Optimization, 21 (2011), 212.
doi: 10.1137/080743573. |
[24] |
J. Nocedal and S. J. Wright, "Numerical Optimization,", $2^{nd}$ edition, (2006).
|
[25] |
K. Sugiki, Y. Narushima and H. Yabe, Globally convergent three-term conjugate gradient methods that use secant conditions and generate descent search directions for unconstrained optimization,, Journal of Optimization Theory and Applications, 153 (2012), 733.
doi: 10.1007/s10957-011-9960-x. |
[26] |
W. Sun and Y. Yuan, "Optimization Theory and Methods: Nonlinear Programming,", Springer, (2006).
|
[27] |
G. Yu, L. Guan and W. Chen, Spectral conjugate gradient methods with sufficient descent property for large-scale unconstrained optimization,, Optimization Methods and Software, 23 (2008), 275.
doi: 10.1080/10556780701661344. |
[28] |
G. Yu, L. Guan and G. Li, Global convergence of modified Polak-Ribière-Polyak conjugate gradient methods with sufficient descent property,, Journal of Industrial and Management Optimization, 4 (2008), 565.
doi: 10.3934/jimo.2008.4.565. |
[29] |
G. Yuan, Modified nonlinear conjugate gradient methods with sufficient descent property for large-scale optimization problems,, Optimization Letters, 3 (2009), 11.
doi: 10.1007/s11590-008-0086-5. |
[30] |
L. Zhang and J. Li, A new globalization technique for nonlinear conjugate gradient methods for nonconvex minimization,, Applied Mathematics and Computation, 217 (2011), 10295.
doi: 10.1016/j.amc.2011.05.032. |
[31] |
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.
doi: 10.1007/s00211-006-0028-z. |
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