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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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2016-04-13 10:10:38
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Restricted Document
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12912
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UniSZA
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[1] 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 [2] 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 [3] E. Polak and G. Ribiere, Note Sur la convergence de directions conjuge`es, ESAIM: Mathematical Modelling and Numerical Analysis, 3E (1969), 35-43. [4] 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 [5] R. Fletcher, Practical Method of Optimization, 2 ed., vol. I, New York, 2000. http://dx.doi.org/10.1002/9781118723203 [6] 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 [7] Y.-H. Dai and Y.-X. 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 [8] M. J. D. Powell, Restart procedures for the conjugate gradient method, Mathematical Programming, 12 (1977), 241–254. http://dx.doi.org/10.1007/bf01593790 [9] J. Nocedal and S. J. Wright, Numerical Optimization, Springer, 1999. http://dx.doi.org/10.1007/b98874 [10] 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 [11] L. Guanghui, H. Jiye, and Y. Hongxia, Global convergence of the Fletcher-Reeves algorithm with inexact linesearch, Applied MathematicsA Journal of Chinese Universities, 10 (1995), 75-82. http://dx.doi.org/10.1007/bf02663897 [12] 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 [13] 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 [14] Y.-H. 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 (1998), 345-358. http://dx.doi.org/10.1137/s1052623494268443 [15] P. Wolfe, Convergence conditions for ascent methods, SIAM Review, 11 (1969), 226-235. http://dx.doi.org/10.1137/1011036 [16] H. Liu, A new conjugate gradient method for unconstrained optimization, Far East Journal of Mathematical Sciences (FJMS), 40 (2010), 145-152. [17] M. Rivaie, M. Fauzi and M. Mamat, New modifications of conjugate gradient coefficient with global convergence properties, 2012 IEEE Symposium on Humanities, Science and Engineering Research (SHUSER), Kuala Lumpur, (2012), 625-629. http://dx.doi.org/10.1109/shuser.2012.6268897 [18] A. Y. Al-Bayati, M. S. Al-Salih and M. M. M. Ali, A Modified Family of CG-Algorithm with a New Closed-Form Line-Search Procedure, Australian Journal of Basic & Applied Sciences, 7 (2013), 214-220. [19] A. Abashar, M. Mamat, M. Rivaie, M. Fauzi and Z. Salleh, A modified DPRP conjugate gradient method for unconstrained optimization, Far East Journal of Mathematical Sciences (FJMS), 97 (2015), 31-44. http://dx.doi.org/10.17654/fjmsmay2015_031_044 [20] M. Hamoda, A. Abashar, M. Mamat and M. Rivaie, A comparative study of two new conjugate gradient methods, AIP Conference Proceedings, 1643 (2015), 616-621. http://dx.doi.org/10.1063/1.4907502 [21] A. Abashar, M. Mamat, M. Rivaie and I. Mohd, Global convergence properties of a new class of conjugate gradient method for unconstrained optimization, Applied Mathematical Sciences, 8 (2014), 3307 - 3319. http://dx.doi.org/10.12988/ams.2014.43246 [22] M. Hamoda, M. Rivaie, M. Mamat and Z. Salleh, A New Nonlinear Conjugate Gradient Coefficient for Unconstrained Optimization, Applied Mathematical Sciences, 9 (2015), 1813-1822. http://dx.doi.org/10.12988/ams.2015.411994 [23] M. Hamoda, M. Rivaie, M. Mamat and Z. Salleh, A Conjugate Gradient Method with Inexact Line Search for Unconstrained Optimization, Applied Mathematical Sciences, 9 (2015), 1823-1832. http://dx.doi.org/10.12988/ams.2015.411995 [24] R. Jaafar, M. Mamat, M. F. Embong and M. Rivaie, A Comparative Study of Modified BFGS and Scale Modified BFGS, Applied Mathematical Sciences, 5 (2011), 3981-3989. [25] I. S. Mohammed, M. Mamat, A. Abashar, Mohd Rivaie and Zabidin Salleh, A Modified Nonlinear Conjugate Gradient Method for Unconstrained Optimization, Applied Mathematical Sciences, 9 (2015), 2671-2682. http://dx.doi.org/10.12988/ams.2015.5141 [26] M. Rivaie, A. Abashar, M. Mamat and I. Mohd, The convergence properties of a new type of conjugate gradient methods, Applied Mathematical Sciences, 8 (2014), 33-44. http://dx.doi.org/10.12988/ams.2014.310578 [27] M. Rivaie, M. Mamat, W. J. Leong and I. Mohd, 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 [28] J. Wang and X. Chi, CG Global Convergence Properties with Goldstein Linesearch*, Bulletin of the Brazilian Mathematical Society, 36 (2005), 197-204. http://dx.doi.org/10.1007/s00574-005-0036-0 [29] M. Mamat, M. Rivaie, I. Mohd and M. Fauzi, A New Conjugate Gradient Coefficient for Unconstrained Optimization, Int. J. Contemp. Math. Scien- ces, 5 (2010), 1429 - 1437. [30] O. Omer, M. Mamat and M. Rivaie, The global convergence properties of a family of conjugate gradient method under the strong wolfe line search, Abstract and Applied Analysis, 2015. [31] Z.-X. Wei, S. W. Yao and L. Y. Liu, The convergence properties of some new conjugate gradient methods, Applied Mathematics and Computation, 183 (2006), 1341-1350. http://dx.doi.org/10.1016/j.amc.2006.05.150 [32] Z.-F. Dai and F. Wen, 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 [33] Y.-Q. Zhang, H. Zheng and C.-L. Zhang, Global Convergence of a Modified PRP Conjugate Gradient Method, Procedia Engineering, 31 (2012), 986-995. http://dx.doi.org/10.1016/j.proeng.2012.01.1131 [34] G. Zoutendijk, Nonlinear Programming, Computational Methods, Chapter in Integer and Nonlinear Programming, North-Holland, Amsterdam, 1970, 37-86. [35] 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 [36] Z.-X. 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 [37] N. Andrei, An unconstrained optimization test functions collection, Advanced Modeling and Optimization, 10 (2008), 147-161. [38] M. Molga and C. Smutnicki, Test Functions for Optimization Needs, 2005. [39] S. Mishra, Some new test functions for global optimization and performance of repulsive particle swarm method, Munich Personal RePEc Archive, Apr 13 2007. [40] 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
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12912 https://intelek.unisza.edu.my/intelek/pages/view.php?ref=12912 https://intelek.unisza.edu.my/intelek/pages/search.php?search=!collection407072 Restricted Document Article Journal image/jpeg inches 96 96 norman 1418 763 47 47 1418x763 2016-04-13 10:10:38 7219-01-FH02-FIK-16-05684.jpg UniSZA Private Access A conjugate gradient method with Strong Wolfe-Powell line search for unconstrained optimization Applied Mathematical Sciences In this paper, a modified conjugate gradient method is presented for solving large-scale unconstrained optimization problems, which possesses the sufficient descent property with Strong Wolfe-Powell line search. A global convergence result was proved when the (SWP) line search was used under some conditions. Computational results for a set consisting of 138 unconstrained optimization test problems showed that this new conjugate gradient algorithm seems to converge more stable and is superior to other similar methods in many situations. 10 13 Hikari Ltd. Hikari Ltd. 721-734 [1] 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 [2] 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 [3] E. Polak and G. Ribiere, Note Sur la convergence de directions conjuge`es, ESAIM: Mathematical Modelling and Numerical Analysis, 3E (1969), 35-43. [4] 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 [5] R. Fletcher, Practical Method of Optimization, 2 ed., vol. I, New York, 2000. http://dx.doi.org/10.1002/9781118723203 [6] 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 [7] Y.-H. Dai and Y.-X. 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 [8] M. J. D. Powell, Restart procedures for the conjugate gradient method, Mathematical Programming, 12 (1977), 241–254. http://dx.doi.org/10.1007/bf01593790 [9] J. Nocedal and S. J. Wright, Numerical Optimization, Springer, 1999. http://dx.doi.org/10.1007/b98874 [10] 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 [11] L. Guanghui, H. Jiye, and Y. Hongxia, Global convergence of the Fletcher-Reeves algorithm with inexact linesearch, Applied MathematicsA Journal of Chinese Universities, 10 (1995), 75-82. http://dx.doi.org/10.1007/bf02663897 [12] 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 [13] 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 [14] Y.-H. 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 (1998), 345-358. http://dx.doi.org/10.1137/s1052623494268443 [15] P. Wolfe, Convergence conditions for ascent methods, SIAM Review, 11 (1969), 226-235. http://dx.doi.org/10.1137/1011036 [16] H. Liu, A new conjugate gradient method for unconstrained optimization, Far East Journal of Mathematical Sciences (FJMS), 40 (2010), 145-152. [17] M. Rivaie, M. Fauzi and M. Mamat, New modifications of conjugate gradient coefficient with global convergence properties, 2012 IEEE Symposium on Humanities, Science and Engineering Research (SHUSER), Kuala Lumpur, (2012), 625-629. http://dx.doi.org/10.1109/shuser.2012.6268897 [18] A. Y. Al-Bayati, M. S. Al-Salih and M. M. M. Ali, A Modified Family of CG-Algorithm with a New Closed-Form Line-Search Procedure, Australian Journal of Basic & Applied Sciences, 7 (2013), 214-220. [19] A. Abashar, M. Mamat, M. Rivaie, M. Fauzi and Z. Salleh, A modified DPRP conjugate gradient method for unconstrained optimization, Far East Journal of Mathematical Sciences (FJMS), 97 (2015), 31-44. http://dx.doi.org/10.17654/fjmsmay2015_031_044 [20] M. Hamoda, A. Abashar, M. Mamat and M. Rivaie, A comparative study of two new conjugate gradient methods, AIP Conference Proceedings, 1643 (2015), 616-621. http://dx.doi.org/10.1063/1.4907502 [21] A. Abashar, M. Mamat, M. Rivaie and I. Mohd, Global convergence properties of a new class of conjugate gradient method for unconstrained optimization, Applied Mathematical Sciences, 8 (2014), 3307 - 3319. http://dx.doi.org/10.12988/ams.2014.43246 [22] M. Hamoda, M. Rivaie, M. Mamat and Z. Salleh, A New Nonlinear Conjugate Gradient Coefficient for Unconstrained Optimization, Applied Mathematical Sciences, 9 (2015), 1813-1822. http://dx.doi.org/10.12988/ams.2015.411994 [23] M. Hamoda, M. Rivaie, M. Mamat and Z. Salleh, A Conjugate Gradient Method with Inexact Line Search for Unconstrained Optimization, Applied Mathematical Sciences, 9 (2015), 1823-1832. http://dx.doi.org/10.12988/ams.2015.411995 [24] R. Jaafar, M. Mamat, M. F. Embong and M. Rivaie, A Comparative Study of Modified BFGS and Scale Modified BFGS, Applied Mathematical Sciences, 5 (2011), 3981-3989. [25] I. S. Mohammed, M. Mamat, A. Abashar, Mohd Rivaie and Zabidin Salleh, A Modified Nonlinear Conjugate Gradient Method for Unconstrained Optimization, Applied Mathematical Sciences, 9 (2015), 2671-2682. http://dx.doi.org/10.12988/ams.2015.5141 [26] M. Rivaie, A. Abashar, M. Mamat and I. Mohd, The convergence properties of a new type of conjugate gradient methods, Applied Mathematical Sciences, 8 (2014), 33-44. http://dx.doi.org/10.12988/ams.2014.310578 [27] M. Rivaie, M. Mamat, W. J. Leong and I. Mohd, 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 [28] J. Wang and X. Chi, CG Global Convergence Properties with Goldstein Linesearch*, Bulletin of the Brazilian Mathematical Society, 36 (2005), 197-204. http://dx.doi.org/10.1007/s00574-005-0036-0 [29] M. Mamat, M. Rivaie, I. Mohd and M. Fauzi, A New Conjugate Gradient Coefficient for Unconstrained Optimization, Int. J. Contemp. Math. Scien- ces, 5 (2010), 1429 - 1437. [30] O. Omer, M. Mamat and M. Rivaie, The global convergence properties of a family of conjugate gradient method under the strong wolfe line search, Abstract and Applied Analysis, 2015. [31] Z.-X. Wei, S. W. Yao and L. Y. Liu, The convergence properties of some new conjugate gradient methods, Applied Mathematics and Computation, 183 (2006), 1341-1350. http://dx.doi.org/10.1016/j.amc.2006.05.150 [32] Z.-F. Dai and F. Wen, 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 [33] Y.-Q. Zhang, H. Zheng and C.-L. Zhang, Global Convergence of a Modified PRP Conjugate Gradient Method, Procedia Engineering, 31 (2012), 986-995. http://dx.doi.org/10.1016/j.proeng.2012.01.1131 [34] G. Zoutendijk, Nonlinear Programming, Computational Methods, Chapter in Integer and Nonlinear Programming, North-Holland, Amsterdam, 1970, 37-86. [35] 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 [36] Z.-X. 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 [37] N. Andrei, An unconstrained optimization test functions collection, Advanced Modeling and Optimization, 10 (2008), 147-161. [38] M. Molga and C. Smutnicki, Test Functions for Optimization Needs, 2005. [39] S. Mishra, Some new test functions for global optimization and performance of repulsive particle swarm method, Munich Personal RePEc Archive, Apr 13 2007. [40] 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
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| spellingShingle |
A conjugate gradient method with Strong Wolfe-Powell line search for unconstrained optimization
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| summary |
In this paper, a modified conjugate gradient method is presented for solving large-scale unconstrained optimization problems, which possesses the sufficient descent property with Strong Wolfe-Powell line search. A global convergence result was proved when the (SWP) line search was used under some conditions. Computational results for a set consisting of 138 unconstrained optimization test problems showed that this new conjugate gradient algorithm seems to converge more stable and is superior to other similar methods in many situations.
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| title |
A conjugate gradient method with Strong Wolfe-Powell line search for unconstrained optimization
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| title_full |
A conjugate gradient method with Strong Wolfe-Powell line search for unconstrained optimization
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| title_fullStr |
A conjugate gradient method with Strong Wolfe-Powell line search for unconstrained optimization
|
| title_full_unstemmed |
A conjugate gradient method with Strong Wolfe-Powell line search for unconstrained optimization
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| title_short |
A conjugate gradient method with Strong Wolfe-Powell line search for unconstrained optimization
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| title_sort |
conjugate gradient method with strong wolfe-powell line search for unconstrained optimization
|