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INTELEK Repository
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Online Access
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https://intelek.unisza.edu.my/intelek/pages/search.php?search=!collection407072
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2024-08-26 17:57:06
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11949
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[1] A. Abashar, M. Mustafa, M Rivaie and M. Ismail, The proof of sufficient descent condition for a new type of conjugate gradient method, AIP Conf. Proc. 296 1602 (2014); http://dx.doi.org/10.1063/1.4882502 [2] 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 [3] D. Touati-Ahmed, C. Storey, Efficient hybrid conjugate gradient techniques, J. Optim. Theory Appl. 64 (1990), 379–397. http://dx.doi.org/10.1007/bf00939455 [4] E. Dolan, J.J. More, Benchmarking optimization software with performance profile, Math. Prog. 91 (2002), 201–213. http://dx.doi.org/10.1007/s101070100263 [5] E. Polak and G. Ribière, Note sur la convergence de directions conjuguée, Rev. Francaise Informat Recherche Operationelle, 3e Année 16 (1969), 35-43. [6] G. H. Liu, J. Y. Han, and H. X. Yin, Global convergence of the FletcherReeves algorithm with an inexact line search, Report, Institute of Applied Mathematics, Chinese Academy of Sciences, Beijing, 1993. [7] G. Zoutendijk, Nonlinear programming, computational methods, in Integer and Nonlinear Programming, J. Abadie, ed., North- Holland, Amsterdam, (1970), 37-86. [8] 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 [9] J. Sun, J Zhang, Global convergence of conjugate gradient methods without line search, Ann. Oper. Res. 103 (2001), 161-173. [10] M. Al-Baali, Descent property and global convergence of the FletcherReeves method with inexact line search, IMA J. Numer. Anal. 5 (1985), 121-124. http://dx.doi.org/10.1093/imanum/5.1.121 [11] M.J.D. Powell, Convergence properties of algorithm for nonlinear optimization, SIAM Rev. 28 (1986), 487-500. http://dx.doi.org/10.1137/1028154 [12] M.J.D. Powell, Restart procedures for the conjugate gradient method, Math. Program. 12 (1977), 241-254. http://dx.doi.org/10.1007/bf01593790 [13] M. R. Hestenes and E. L. Stiefel, Methods of conjugate gradients for solving linear systems, J. Research Nat. Bur. Standard. 49 (1952), 409-436. http://dx.doi.org/10.6028/jres.049.044 [14] 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. 218 (2012), 11323-11332. http://dx.doi.org/10.1016/j.amc.2012.05.030 [15] N. Andrei, An unconstrained optimization test functions collection, Advanced Modelling and optimization 10(1) (2008), 147-161. [16] N. Andrei, Accelerated conjugate gradient algorithm with finite difference Hessian / vector product approximation for unconstrained optimization. J. comput. Appl. Math. 230 (2009), 570–582. http://dx.doi.org/10.1016/j.cam.2008.12.024 [17] R. Fletcher, Practical Method of Optimization, Vol. 1, Unconstrained Optimization, John Wiley & Sons, New York, 1987. [18] R. Fletcher and C. Reeves, Function minimization by conjugate gradients, Comput. J. 7 (1964), 149-154. http://dx.doi.org/10.1093/comjnl/7.2.149 [19] W.W. Hager, and H.C. Zhang, A new conjugate gradient method with guaranteed descent and efficient line search. SIAM J. Optim. 16 (2005), 170–192. 1868 Ibrahim S. Mohammed et al. http://dx.doi.org/10.1137/030601880 [20] Y. F. Hu and C. Storey, Global convergence result for conjugate gradient methods, J. Optim. Theory Appl. 71 (1991), 399–405. http://dx.doi.org/10.1007/bf00939927 [21] Y.H. Dai, Y. Yuan, A nonlinear conjugate gradient method with a strong global convergence properties, SIAM J. Optim. 10 (1999), 177-182. http://dx.doi.org/10.1137/s1052623497318992 [22] Y.H Dai, Y. Yuan, Nonlinear Conjugate Gradient Method, Shanghai Scientific and Technical Publisher, Beijing, 1998. [23] Y. Liu, C. Storey, Efficient generalized conjugate gradient algorithms part 1: Theory, J. Comput. Appl. Math. 69 (1991), 129-137. http://dx.doi.org/10.1007/bf00940464 [24] Y. Yuan, and W. Sun, Theory and Methods of Optimization. Science press of China, Beijing, 1999. [25] Z. Wei, Y. Shengwei, and L. Linging, The convergence properties of some new conjugate gradient methods. Appl. Math. Comput. 183 (2006), 1341-1350. http://dx.doi.org/10.1016/j.amc.2006.05.150
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6250-01-FH02-FIK-15-03343.pdf
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11949 https://intelek.unisza.edu.my/intelek/pages/view.php?ref=11949 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 win7 Win7 2024-08-26 17:57:06 6250-01-FH02-FIK-15-03343.pdf UniSZA Private Access The Global Convergence Properties of an Improved Conjugate Gradient Method Applied Mathematical Sciences Conjugate gradient (CG) methods have played a significant role in solving large scale unconstrained optimization. This is due to its simplicity, low memory requirement, and global convergence properties. Various studies and modifications have been done recently to improve this method. In this paper, we proposed a new conjugate gradient parameter ( ) k which possesses global convergence properties under the exact line search. Numerical result shows that our new formula performs better when compared to other classical conjugate gradient methods. 9 38 HIKARI Ltd. HIKARI Ltd. 1857-1868 [1] A. Abashar, M. Mustafa, M Rivaie and M. Ismail, The proof of sufficient descent condition for a new type of conjugate gradient method, AIP Conf. Proc. 296 1602 (2014); http://dx.doi.org/10.1063/1.4882502 [2] 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 [3] D. Touati-Ahmed, C. Storey, Efficient hybrid conjugate gradient techniques, J. Optim. Theory Appl. 64 (1990), 379–397. http://dx.doi.org/10.1007/bf00939455 [4] E. Dolan, J.J. More, Benchmarking optimization software with performance profile, Math. Prog. 91 (2002), 201–213. http://dx.doi.org/10.1007/s101070100263 [5] E. Polak and G. Ribière, Note sur la convergence de directions conjuguée, Rev. Francaise Informat Recherche Operationelle, 3e Année 16 (1969), 35-43. [6] G. H. Liu, J. Y. Han, and H. X. Yin, Global convergence of the FletcherReeves algorithm with an inexact line search, Report, Institute of Applied Mathematics, Chinese Academy of Sciences, Beijing, 1993. [7] G. Zoutendijk, Nonlinear programming, computational methods, in Integer and Nonlinear Programming, J. Abadie, ed., North- Holland, Amsterdam, (1970), 37-86. [8] 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 [9] J. Sun, J Zhang, Global convergence of conjugate gradient methods without line search, Ann. Oper. Res. 103 (2001), 161-173. [10] M. Al-Baali, Descent property and global convergence of the FletcherReeves method with inexact line search, IMA J. Numer. Anal. 5 (1985), 121-124. http://dx.doi.org/10.1093/imanum/5.1.121 [11] M.J.D. Powell, Convergence properties of algorithm for nonlinear optimization, SIAM Rev. 28 (1986), 487-500. http://dx.doi.org/10.1137/1028154 [12] M.J.D. Powell, Restart procedures for the conjugate gradient method, Math. Program. 12 (1977), 241-254. http://dx.doi.org/10.1007/bf01593790 [13] M. R. Hestenes and E. L. Stiefel, Methods of conjugate gradients for solving linear systems, J. Research Nat. Bur. Standard. 49 (1952), 409-436. http://dx.doi.org/10.6028/jres.049.044 [14] 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. 218 (2012), 11323-11332. http://dx.doi.org/10.1016/j.amc.2012.05.030 [15] N. Andrei, An unconstrained optimization test functions collection, Advanced Modelling and optimization 10(1) (2008), 147-161. [16] N. Andrei, Accelerated conjugate gradient algorithm with finite difference Hessian / vector product approximation for unconstrained optimization. J. comput. Appl. Math. 230 (2009), 570–582. http://dx.doi.org/10.1016/j.cam.2008.12.024 [17] R. Fletcher, Practical Method of Optimization, Vol. 1, Unconstrained Optimization, John Wiley & Sons, New York, 1987. [18] R. Fletcher and C. Reeves, Function minimization by conjugate gradients, Comput. J. 7 (1964), 149-154. http://dx.doi.org/10.1093/comjnl/7.2.149 [19] W.W. Hager, and H.C. Zhang, A new conjugate gradient method with guaranteed descent and efficient line search. SIAM J. Optim. 16 (2005), 170–192. 1868 Ibrahim S. Mohammed et al. http://dx.doi.org/10.1137/030601880 [20] Y. F. Hu and C. Storey, Global convergence result for conjugate gradient methods, J. Optim. Theory Appl. 71 (1991), 399–405. http://dx.doi.org/10.1007/bf00939927 [21] Y.H. Dai, Y. Yuan, A nonlinear conjugate gradient method with a strong global convergence properties, SIAM J. Optim. 10 (1999), 177-182. http://dx.doi.org/10.1137/s1052623497318992 [22] Y.H Dai, Y. Yuan, Nonlinear Conjugate Gradient Method, Shanghai Scientific and Technical Publisher, Beijing, 1998. [23] Y. Liu, C. Storey, Efficient generalized conjugate gradient algorithms part 1: Theory, J. Comput. Appl. Math. 69 (1991), 129-137. http://dx.doi.org/10.1007/bf00940464 [24] Y. Yuan, and W. Sun, Theory and Methods of Optimization. Science press of China, Beijing, 1999. [25] Z. Wei, Y. Shengwei, and L. Linging, The convergence properties of some new conjugate gradient methods. Appl. Math. Comput. 183 (2006), 1341-1350. http://dx.doi.org/10.1016/j.amc.2006.05.150
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| spellingShingle |
The Global Convergence Properties of an Improved Conjugate Gradient Method
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| summary |
Conjugate gradient (CG) methods have played a significant role in solving large scale unconstrained optimization. This is due to its simplicity, low memory requirement, and global convergence properties. Various studies and modifications have been done recently to improve this method. In this paper, we proposed a new conjugate gradient parameter ( ) k which possesses global convergence properties under the exact line search. Numerical result shows that our new formula performs better when compared to other classical conjugate gradient methods.
|
| title |
The Global Convergence Properties of an Improved Conjugate Gradient Method
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| title_full |
The Global Convergence Properties of an Improved Conjugate Gradient Method
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| title_fullStr |
The Global Convergence Properties of an Improved Conjugate Gradient Method
|
| title_full_unstemmed |
The Global Convergence Properties of an Improved Conjugate Gradient Method
|
| title_short |
The Global Convergence Properties of an Improved Conjugate Gradient Method
|
| title_sort |
global convergence properties of an improved conjugate gradient method
|