Another Modified Conjugate Gradient Coefficient with Global Convergence Properties
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| internalnotes | [1] E. Stiefel, M. R Hestenes, Method of conjugate gradient for solving linear equation, J. Res. Nat. Bur. Stand. 49(1952), 409-436. http://dx.doi.org/10.6028/jres.049.044 [2] C. Reeves, R. Fletcher, Function minimization by conjugate gradients, Computer J. 7(1964)149-154. http://dx.doi.org/10.1093/comjnl/7.2.149 [3] B.T. Polyak, The conjugate gradient method in extreme problems, USSR Comp. Math. Phys. 9(1969), 94-112. http://dx.doi.org/10.1016/0041-5553(69)90035-4 [4] E. Polak and G. Ribière Note sur la convergence de directions conjuguée, Rev. Francaise Informat Recherche Operationelle, 3e Année. 16 (1969), 35-43. [5] M. Rivaie, M Mamat, W.J. Leong and M. Ismail, A new class of nonlinear conjugate gradient coefficients with global convergence properties, Applied Mathematics and Computation 2189(2012), 11323-11332. http://dx.doi.org/10.1016/j.amc.2012.05.030 [6] Zengxin Wei, Shengwei Yao, Liying Liu, The convergence properties of some new conjugate gradient methods, Appl. Math and Comput. 183(2006), 1341-1350. http://dx.doi.org/10.1016/j.amc.2006.05.150 [7] N. Andrei, An unconstrained optimization test functions collection, Advanced Modelling and Optimization 10 (1)(2008), 147-161. [8] Y. Dai, Y. Yuan, A nonlinear conjugate gradient with strong global convergence properties, SIAM. 10(2000), 177-182. http://dx.doi.org/10.1137/s1052623497318992 [9] E. Dolan, J. J. More, Benchmarking Optimization software with performance profile, Math. Prog. 91(2002), 201-213. http://dx.doi.org/10.1007/s101070100263 [10] G. Zoutendijk, Nonlinear programming, computational methods, in:, J. Abadie, (Ed). Integer and Nonlinear Programming, North-Holland, Amsterdam, 1970, pp. 37-86. [11] G. H. Liu, J. Y. Han, and H. X. Yin, Global convergence of the Fletcher Reeves algorithm with an inexact line search, Report, Institute of Applied Mathematics, Chinese Academy of Sciences, Beijing, 1993. [12] Abashar, M Mamat, M Rivaie and Ismail, Global convergence properties of a new class of conjugate gradient method for unconstrained optimization, Applied Mathematics and Computation Vol 8(2014), no 1, 3307-3319. [13] M. J. D. Powell, Non-convex minimization calculations and the conjugate gradient method in Lecture notes in mathematics 1066, Springer-Verlag, Berlin, 1984, pp. 122-241. http://dx.doi.org/10.1007/bfb0099521 [14] M. Rivaie, M Mamat, W.J. Leong and M. Fauzi, A comparative study of conjugate gradient coefficient for unconstrained optimization, Aus. J. Bas. Appl. Sci. 5(2011), 947-951. [15] F. Wen, Z. Dai, Another improved Wei-Yao-Liu nonlinear conjugate gradient method with sufficient descent property, Applied Mathematics and Computation 218(2012), 7421-7430. http://dx.doi.org/10.1016/j.amc.2011.12.091 [16] H. C. Zhang, W. W. Hager, A new conjugate gradient method with guaranteed descent and efficient line search, SIAM J. Optim. 16(2005), 170-192. http://dx.doi.org/10.1137/030601880 [17] J. C. Gilbert and J. Nocedal, Global convergence properties of conjugate gradient methods for optimization, SIAM J. Optim. 2(1992), 21-42. http://dx.doi.org/10.1137/0802003 [18] M. Al-Baali, Descent property and global convergence of the Fletcher-Reeves method with inexact line search, IMA J. Numer. Anal. 5(1985), 121-124. http://dx.doi.org/10.1093/imanum/5.1.121 [19] C. Story, Y. Liu, Efficient generalized conjugate gradient algorithms part 1: Theory, J. Optim. Theory Appl. Math. 69(1992), 129-137. http://dx.doi.org/10.1007/bf00940464 [20] Sha Lu, Zengxin W. and Lilio Mo, Some global convergent of the Wei-Yao-Liu conjugate gradient method with inexact line search, Applied Mathematics and Computation 217(2011) 7132-7137. http://dx.doi.org/10.1016/j.amc.2011.01.097 [21] K. E. Hilstrom, A simulation test approach to the evalution of nonlinear optimization algoriths, Acm. Trans. Math. Softw. 3(1977), 305-315. http://dx.doi.org/10.1145/355759.355760 [22] M. Rivaie, M Mamat, W.J. Leong and M Ismail, A New conjugate gradient coefficient for large scale nonlinear unconstrained optimization, Int. Journal of Math. Analysis, Vol. 6(2012), 23, 1131-1146. |
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| spelling | 15222 https://intelek.unisza.edu.my/intelek/pages/view.php?ref=15222 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 13 1.6 User user USER UsEr 2024-08-30 11:13:07 5983-01-FH02-FIK-15-03246.pdf UniSZA Private Access Another Modified Conjugate Gradient Coefficient with Global Convergence Properties Applied Mathematical Sciences Conjugate gradient [CG] methods are considered in solving nonlinear unconstrained optimization problem, because of their simplicity, low memory requirement and global convergence properties. Different reviews and modification have been carried out in order to upgrade the method. In this paper, a new type of CG parameter, which satisfies the sufficient descent condition and global convergences property under exact line search, is proposed. The numerical outcomes indicate that our new modified parameter perform well when compare with other CG parameters for a given standards test function. 9 37 HIKARI Ltd. HIKARI Ltd. 1833-1844 [1] E. Stiefel, M. R Hestenes, Method of conjugate gradient for solving linear equation, J. Res. Nat. Bur. Stand. 49(1952), 409-436. http://dx.doi.org/10.6028/jres.049.044 [2] C. Reeves, R. Fletcher, Function minimization by conjugate gradients, Computer J. 7(1964)149-154. http://dx.doi.org/10.1093/comjnl/7.2.149 [3] B.T. Polyak, The conjugate gradient method in extreme problems, USSR Comp. Math. Phys. 9(1969), 94-112. http://dx.doi.org/10.1016/0041-5553(69)90035-4 [4] E. Polak and G. Ribière Note sur la convergence de directions conjuguée, Rev. Francaise Informat Recherche Operationelle, 3e Année. 16 (1969), 35-43. [5] M. Rivaie, M Mamat, W.J. Leong and M. Ismail, A new class of nonlinear conjugate gradient coefficients with global convergence properties, Applied Mathematics and Computation 2189(2012), 11323-11332. http://dx.doi.org/10.1016/j.amc.2012.05.030 [6] Zengxin Wei, Shengwei Yao, Liying Liu, The convergence properties of some new conjugate gradient methods, Appl. Math and Comput. 183(2006), 1341-1350. http://dx.doi.org/10.1016/j.amc.2006.05.150 [7] N. Andrei, An unconstrained optimization test functions collection, Advanced Modelling and Optimization 10 (1)(2008), 147-161. [8] Y. Dai, Y. Yuan, A nonlinear conjugate gradient with strong global convergence properties, SIAM. 10(2000), 177-182. http://dx.doi.org/10.1137/s1052623497318992 [9] E. Dolan, J. J. More, Benchmarking Optimization software with performance profile, Math. Prog. 91(2002), 201-213. http://dx.doi.org/10.1007/s101070100263 [10] G. Zoutendijk, Nonlinear programming, computational methods, in:, J. Abadie, (Ed). Integer and Nonlinear Programming, North-Holland, Amsterdam, 1970, pp. 37-86. [11] G. H. Liu, J. Y. Han, and H. X. Yin, Global convergence of the Fletcher Reeves algorithm with an inexact line search, Report, Institute of Applied Mathematics, Chinese Academy of Sciences, Beijing, 1993. [12] Abashar, M Mamat, M Rivaie and Ismail, Global convergence properties of a new class of conjugate gradient method for unconstrained optimization, Applied Mathematics and Computation Vol 8(2014), no 1, 3307-3319. [13] M. J. D. Powell, Non-convex minimization calculations and the conjugate gradient method in Lecture notes in mathematics 1066, Springer-Verlag, Berlin, 1984, pp. 122-241. http://dx.doi.org/10.1007/bfb0099521 [14] M. Rivaie, M Mamat, W.J. Leong and M. Fauzi, A comparative study of conjugate gradient coefficient for unconstrained optimization, Aus. J. Bas. Appl. Sci. 5(2011), 947-951. [15] F. Wen, Z. Dai, Another improved Wei-Yao-Liu nonlinear conjugate gradient method with sufficient descent property, Applied Mathematics and Computation 218(2012), 7421-7430. http://dx.doi.org/10.1016/j.amc.2011.12.091 [16] H. C. Zhang, W. W. Hager, A new conjugate gradient method with guaranteed descent and efficient line search, SIAM J. Optim. 16(2005), 170-192. http://dx.doi.org/10.1137/030601880 [17] J. C. Gilbert and J. Nocedal, Global convergence properties of conjugate gradient methods for optimization, SIAM J. Optim. 2(1992), 21-42. http://dx.doi.org/10.1137/0802003 [18] M. Al-Baali, Descent property and global convergence of the Fletcher-Reeves method with inexact line search, IMA J. Numer. Anal. 5(1985), 121-124. http://dx.doi.org/10.1093/imanum/5.1.121 [19] C. Story, Y. Liu, Efficient generalized conjugate gradient algorithms part 1: Theory, J. Optim. Theory Appl. Math. 69(1992), 129-137. http://dx.doi.org/10.1007/bf00940464 [20] Sha Lu, Zengxin W. and Lilio Mo, Some global convergent of the Wei-Yao-Liu conjugate gradient method with inexact line search, Applied Mathematics and Computation 217(2011) 7132-7137. http://dx.doi.org/10.1016/j.amc.2011.01.097 [21] K. E. Hilstrom, A simulation test approach to the evalution of nonlinear optimization algoriths, Acm. Trans. Math. Softw. 3(1977), 305-315. http://dx.doi.org/10.1145/355759.355760 [22] M. Rivaie, M Mamat, W.J. Leong and M Ismail, A New conjugate gradient coefficient for large scale nonlinear unconstrained optimization, Int. Journal of Math. Analysis, Vol. 6(2012), 23, 1131-1146. |
| spellingShingle | Another Modified Conjugate Gradient Coefficient with Global Convergence Properties |
| summary | Conjugate gradient [CG] methods are considered in solving nonlinear unconstrained optimization problem, because of their simplicity, low memory requirement and global convergence properties. Different reviews and modification have been carried out in order to upgrade the method. In this paper, a new type of CG parameter, which satisfies the sufficient descent condition and global convergences property under exact line search, is proposed. The numerical outcomes indicate that our new modified parameter perform well when compare with other CG parameters for a given standards test function. |
| title | Another Modified Conjugate Gradient Coefficient with Global Convergence Properties |
| title_full | Another Modified Conjugate Gradient Coefficient with Global Convergence Properties |
| title_fullStr | Another Modified Conjugate Gradient Coefficient with Global Convergence Properties |
| title_full_unstemmed | Another Modified Conjugate Gradient Coefficient with Global Convergence Properties |
| title_short | Another Modified Conjugate Gradient Coefficient with Global Convergence Properties |
| title_sort | another modified conjugate gradient coefficient with global convergence properties |