A conjugate gradient method with inexact line search for unconstrained optimization
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| internalnotes | [1] M. Al-Baali, "Descent Property and Global Convergence of the FletcherReeves Method with Inexact Line Search," IMA Journal of Numerical Analysis, 5 (1985), 121-124. http://dx.doi.org/10.1093/imanum/5.1.121 [2] N. Andrei, "An unconstrained optimization test functions collection," Advanced Modeling and Optimization, 10 (2008), 147-161. [3] Y. Dai, J. Han, G. Liu, D. Sun, H. Yin, and Y.-X. Yuan, "Convergence Properties of Nonlinear Conjugate Gradient Methods," SIAM Journal on Optimization, 10 (2000), 345-358. http://dx.doi.org/10.1137/s1052623494268443 [4] Y. H. Dai and Y. Yuan, "Convergence properties of the Fletcher-Reeves method," IMA Journal of Numerical Analysis, 16 (1996), 155-164. http://dx.doi.org/10.1093/imanum/16.2.155 [5] Y. H. Dai and Y. Yuan, "A nonlinear conjugate gradient method with a strong global convergence property," SIAM Journal on Optimization, 10 (1999), 177- 182. http://dx.doi.org/10.1137/s1052623497318992 [6] E. D. Dolan and J. J. Mor, "Benchmarking optimization software with performance profiles," Mathematical Programming, 91 (2002), 201-213. http://dx.doi.org/10.1007/s101070100263 [7] R. Fletcher, Practical Method of Optimization, 2 ed. I. New York, 1987. http://dx.doi.org/10.1002/9781118723203 [8] R. Fletcher and C. M. Reeves, "Function minimization by conjugate gradients," The Computer Journal, 7 (1964), 149-154. http://dx.doi.org/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. http://dx.doi.org/10.1137/0802003 [10] L. Guanghui, H. Jiye, and Y. Hongxia, "Global convergence of the fletcherreeves algorithm with inexact linesearch," Applied Mathematics-A Journal of Chinese Universities, 10 (1995), 75-82. http://dx.doi.org/10.1007/bf02663897 [11] 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), 409-436. http://dx.doi.org/10.6028/jres.049.044 [12] Y. F. Hu and C. Storey, "Global Convergence Result for Conjugate-Gradient Methods," Journal of Optimization Theory and Applications, 71 (1991), 399-405. http://dx.doi.org/10.1007/bf00939927 [13] S. Jie and Z. Jiapu, "Global Convergence of Conjugate Gradient Methods without Line Search," Annals of Operations Research, 103 (2001), 161–173. http://dx.doi.org/10.1023/a:1012903105391 [14] G. Y. Li, C. M. Tang, and Z. X. Wei, "New conjugacy condition and related new conjugate gradient methods for unconstrained optimization," Journal of Computational and Applied Mathematics, 202 (2007), 523-539. http://dx.doi.org/10.1016/j.cam.2006.03.005 [15] Y. Liu and C. Storey, "Efficient generalized conjugate gradient algorithms, Part 1: Theory," Journal of Optimization Theory and Applications, 69 (1991), 129-137. http://dx.doi.org/10.1007/bf00940464 [16] J. J. More, B. S. Garboww, and K. E. Hillstrom, "Testing Unconstrained Optimization Software," ACM Transactions on Mathematical Software 7 (1981), 17-41. http://dx.doi.org/10.1145/355934.355936 [17] J. Nocedal and S. J. Wright, Numerical Optimization: Springer, 1999. http://dx.doi.org/10.1007/b98874 [18] E. Polak and G. Ribiere, "Note Sur la convergence de directions conjuge`es," ESAIM: Mathematical Modelling and Numerical Analysis, 3E (1969), 35–43. [19] B. T. Polyak, "The conjugate gradient method in extreme problems," USSR Computational Mathematics and Mathematical Physics, 9 (1969), 94–112. http://dx.doi.org/10.1016/0041-5553(69)90035-4 [20] M. J. D. Powell, "Restart procedures for the conjugate gradient method," Mathematical Programming 12 (1977), 241–254. http://dx.doi.org/10.1007/bf01593790 [21] D. Touati-Ahmed and C. Storey, "Efficient Hybrid Conjugate Gradient Techniques," Journal of optimization theory and applications, 64 (1990), 379- 397. http://dx.doi.org/10.1007/bf00939455 [22] Z. Wei, G. Li, and L. Qi, "New nonlinear conjugate gradient formulas for large-scale unconstrained optimization problems," Applied Mathematics and Computation, 179 (2006), 407-430. http://dx.doi.org/10.1016/j.amc.2005.11.150 [23] P. Wolfe, "Convergence conditions for ascent methods," SIAM Review, 11 (1969), 226-235. http://dx.doi.org/10.1137/1011036 [24] Y. Q. Zhang, H. Zheng, and C. L. Zhang, "Global Convergence of a Modified PRP Conjugate Gradient Method," in International Conference on Advances in Computational Modeling and Simulation, (2012), 986-995. http://dx.doi.org/10.1016/j.proeng.2012.01.1131 [25] G. Zoutendijk, "Nonlinear programming, computational methods," in Integer and nonlinear programming, ed North-Holland, Amsterdam, 1970, pp. 37-86. |
| originalfilename | 6234-01-FH02-FIK-15-03335.pdf |
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| resourceurl | https://intelek.unisza.edu.my/intelek/pages/view.php?ref=11933 |
| spelling | 11933 https://intelek.unisza.edu.my/intelek/pages/view.php?ref=11933 https://intelek.unisza.edu.my/intelek/pages/search.php?search=!collection407072 Restricted Document Article Journal application/pdf Adobe Acrobat Pro DC 20 Paper Capture Plug-in with ClearScan 11 1.6 HP Hp hp 2024-08-26 17:51:40 6234-01-FH02-FIK-15-03335.pdf UniSZA Private Access A conjugate gradient method with inexact line search for unconstrained optimization Applied Mathematical Sciences In this paper, an efficient nonlinear modified PRP conjugate gradient method is presented for solving large-scale unconstrained optimization problems. The sufficient descent property is satisfied under strong Wolfe-Powell (SWP) line search by restricting the parameter 1/ 4 . The global convergence result is established under the (SWP) line search conditions. Numerical results, for a set consisting of 133 unconstrained optimization test problems, show that this method is better than the PRP method and the FR method. 9 37 HIKARI Ltd. HIKARI Ltd. 1823-1832 [1] M. Al-Baali, "Descent Property and Global Convergence of the FletcherReeves Method with Inexact Line Search," IMA Journal of Numerical Analysis, 5 (1985), 121-124. http://dx.doi.org/10.1093/imanum/5.1.121 [2] N. Andrei, "An unconstrained optimization test functions collection," Advanced Modeling and Optimization, 10 (2008), 147-161. [3] Y. Dai, J. Han, G. Liu, D. Sun, H. Yin, and Y.-X. Yuan, "Convergence Properties of Nonlinear Conjugate Gradient Methods," SIAM Journal on Optimization, 10 (2000), 345-358. http://dx.doi.org/10.1137/s1052623494268443 [4] Y. H. Dai and Y. Yuan, "Convergence properties of the Fletcher-Reeves method," IMA Journal of Numerical Analysis, 16 (1996), 155-164. http://dx.doi.org/10.1093/imanum/16.2.155 [5] Y. H. Dai and Y. Yuan, "A nonlinear conjugate gradient method with a strong global convergence property," SIAM Journal on Optimization, 10 (1999), 177- 182. http://dx.doi.org/10.1137/s1052623497318992 [6] E. D. Dolan and J. J. Mor, "Benchmarking optimization software with performance profiles," Mathematical Programming, 91 (2002), 201-213. http://dx.doi.org/10.1007/s101070100263 [7] R. Fletcher, Practical Method of Optimization, 2 ed. I. New York, 1987. http://dx.doi.org/10.1002/9781118723203 [8] R. Fletcher and C. M. Reeves, "Function minimization by conjugate gradients," The Computer Journal, 7 (1964), 149-154. http://dx.doi.org/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. http://dx.doi.org/10.1137/0802003 [10] L. Guanghui, H. Jiye, and Y. Hongxia, "Global convergence of the fletcherreeves algorithm with inexact linesearch," Applied Mathematics-A Journal of Chinese Universities, 10 (1995), 75-82. http://dx.doi.org/10.1007/bf02663897 [11] 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), 409-436. http://dx.doi.org/10.6028/jres.049.044 [12] Y. F. Hu and C. Storey, "Global Convergence Result for Conjugate-Gradient Methods," Journal of Optimization Theory and Applications, 71 (1991), 399-405. http://dx.doi.org/10.1007/bf00939927 [13] S. Jie and Z. Jiapu, "Global Convergence of Conjugate Gradient Methods without Line Search," Annals of Operations Research, 103 (2001), 161–173. http://dx.doi.org/10.1023/a:1012903105391 [14] G. Y. Li, C. M. Tang, and Z. X. Wei, "New conjugacy condition and related new conjugate gradient methods for unconstrained optimization," Journal of Computational and Applied Mathematics, 202 (2007), 523-539. http://dx.doi.org/10.1016/j.cam.2006.03.005 [15] Y. Liu and C. Storey, "Efficient generalized conjugate gradient algorithms, Part 1: Theory," Journal of Optimization Theory and Applications, 69 (1991), 129-137. http://dx.doi.org/10.1007/bf00940464 [16] J. J. More, B. S. Garboww, and K. E. Hillstrom, "Testing Unconstrained Optimization Software," ACM Transactions on Mathematical Software 7 (1981), 17-41. http://dx.doi.org/10.1145/355934.355936 [17] J. Nocedal and S. J. Wright, Numerical Optimization: Springer, 1999. http://dx.doi.org/10.1007/b98874 [18] E. Polak and G. Ribiere, "Note Sur la convergence de directions conjuge`es," ESAIM: Mathematical Modelling and Numerical Analysis, 3E (1969), 35–43. [19] B. T. Polyak, "The conjugate gradient method in extreme problems," USSR Computational Mathematics and Mathematical Physics, 9 (1969), 94–112. http://dx.doi.org/10.1016/0041-5553(69)90035-4 [20] M. J. D. Powell, "Restart procedures for the conjugate gradient method," Mathematical Programming 12 (1977), 241–254. http://dx.doi.org/10.1007/bf01593790 [21] D. Touati-Ahmed and C. Storey, "Efficient Hybrid Conjugate Gradient Techniques," Journal of optimization theory and applications, 64 (1990), 379- 397. http://dx.doi.org/10.1007/bf00939455 [22] Z. Wei, G. Li, and L. Qi, "New nonlinear conjugate gradient formulas for large-scale unconstrained optimization problems," Applied Mathematics and Computation, 179 (2006), 407-430. http://dx.doi.org/10.1016/j.amc.2005.11.150 [23] P. Wolfe, "Convergence conditions for ascent methods," SIAM Review, 11 (1969), 226-235. http://dx.doi.org/10.1137/1011036 [24] Y. Q. Zhang, H. Zheng, and C. L. Zhang, "Global Convergence of a Modified PRP Conjugate Gradient Method," in International Conference on Advances in Computational Modeling and Simulation, (2012), 986-995. http://dx.doi.org/10.1016/j.proeng.2012.01.1131 [25] G. Zoutendijk, "Nonlinear programming, computational methods," in Integer and nonlinear programming, ed North-Holland, Amsterdam, 1970, pp. 37-86. |
| spellingShingle | A conjugate gradient method with inexact line search for unconstrained optimization |
| summary | In this paper, an efficient nonlinear modified PRP conjugate gradient method is presented for solving large-scale unconstrained optimization problems. The sufficient descent property is satisfied under strong Wolfe-Powell (SWP) line search by restricting the parameter 1/ 4 . The global convergence result is established under the (SWP) line search conditions. Numerical results, for a set consisting of 133 unconstrained optimization test problems, show that this method is better than the PRP method and the FR method. |
| title | A conjugate gradient method with inexact line search for unconstrained optimization |
| title_full | A conjugate gradient method with inexact line search for unconstrained optimization |
| title_fullStr | A conjugate gradient method with inexact line search for unconstrained optimization |
| title_full_unstemmed | A conjugate gradient method with inexact line search for unconstrained optimization |
| title_short | A conjugate gradient method with inexact line search for unconstrained optimization |
| title_sort | conjugate gradient method with inexact line search for unconstrained optimization |