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1860797542645628928
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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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| date |
2016-06-30 11:06:47
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Restricted Document
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13169
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UniSZA
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[1] M. R. Hestenes and E. Stiefel, Method of conjugate gradient for solving linear equations, J. Res. Nat. Bur. Stand. 49 (1952), 409-436. [2] A. Al-Baali, Descent property and global convergence of the Fletcher-Reeves method with inexact line search, IMA J. Numer. Anal. 5 (1985), 121-124. [3] Y. Dai and Y. Yuan, Nonlinear Conjugate Gradient Methods, Science Press of Shanghai, Shanghai, 2000. [4] Y. H. Dai and Y. Yuan, A nonlinear conjugate gradient method with a strong global convergent property, SIAM J. Optim. 10 (1999), 177-182. [5] Zhen-Jun Shi and Jinhua Gua, A new family of conjugate gradient methods, J. Comput. Appl. Math. 224 (2009), 444-457. [6] J. C. Gilbert and J. Nocedal, Convergence properties of conjugate gradient methods for optimization, SIAM. J. Optim. 2(1) (1992), 21-42. [7] M. J. D. Powell, Restart procedure for the conjugate gradient method, Math. Prog. 2 (1977), 241-254. [8] M. J. D. Powell, Non-convex minimization calculation and the conjugate gradient method, Lecture Notes in Mathematics, 1066, Springer-Verlag, Berlin, 1984. [9] N. Andrei, An unconstrained optimization test functions collection, Adv. Modell. Optim. 10 (2008), 147-161. [10] G. Zoutendijk, Nonlinear Programming Computational Methods, J. Abadie, ed., Integer and Nonlinear Programming, North Holland, Amsterdam, 1970, pp. 37-86. [11] W. W. Hager and H. Zhang, A new conjugate gradient method with guaranteed descent and an efficient line search, SIAM. Optim. 16 (2005), 170-192. [12] Y. H. Dai and Y. X. Yuan, A nonlinear conjugate gradient with a strong global convergence properties, SIAM J. Optim. 10 (2000), 177-182. [13] L. Zhang, W. J. Zhou and D. H. Li, Global convergence of a modified FletcherReeves conjugate method with Armijo-type line search, Numer. Math. 104 (2006), 561-572. [14] N. Andrei, A modified Polak-Ribiere-Polyak conjugate gradient algorithm for unconstrained optimization, Optimization 60 (2011), 1457-1471. [15] L. Grippo and S. Lucidi, A globally convergent version of the Polak-Ribiere gradient method, Math. Program. 78 (1997), 375-391. [16] M. Rivaie, M. Mamat, L. Wah June and M. Ismail, A new class of nonlinear conjugate gradient coefficients with global convergence properties, Appl. Math. Comput. 218 (2012), 1132-1133. [17] R. Fletcher and C. Reeves, Function minimization by conjugate gradients, Comput. J. 7 (1964), 149-154. [18] M. J. D. Powell, Non-convex minimization calculations and the conjugate gradient method, Lecture Notes in Mathematics, 1066, Springer-Verlag, Berlin, 1984. [19] E. Polak and G. Ribiere, Note Sur la convergence de directions conjugees, Rev. Francaise in Format Recherche Operationelle 3e Annee 16 (1969), 35-43. [20] Li Zhang, An improved Wei-Yao-Liu nonlinear conjugate gradient method for optimization computation, Appl. Math. Comput. 215 (2009), 2269-2274. [21] K. E. Hilstrom, A simulation test approach to the evaluation of nonlinear optimization algorithms, ACM. Trans. Math. Softw. 3 (1977), 305-315. [22] E. Dolan and J. J. More, Benchmarking optimization software with performance profile, Math. Program. 91 (2002), 201-213. [23] Z. Wei, G. Li and L. Qi, New nonlinear conjugate gradient formulas for large-scale unconstrained optimization problems, Appl. Math. Comput. 179 (2006), 407-430. [24] R. Fletcher, Practical Method of Optimization, 2nd ed., Unconstrained Optimization, Vol. I, Wiley, New York, 1997. [25] Y. Liu and C. Storey, Efficient generalized conjugate gradient algorithms. Part 1: Theory, J. Optim. Theory Appl. 69 (1992), 129-137. [26] B. T. Polyak, The conjugate gradient method in extreme problems, USSR Comput. Math. Math. Phys. 9 (1969), 94-112. [27] N. Andrei, 40 conjugate gradient algorithms for unconstrained optimization, Bull. Malay. Math. Sci. Soc. 34 (2011), 319-330.
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13169 https://intelek.unisza.edu.my/intelek/pages/view.php?ref=13169 https://intelek.unisza.edu.my/intelek/pages/search.php?search=!collection407072 Restricted Document Article Journal image/jpeg inches 96 96 norman 1421 770 27 27 1421x770 2016-06-30 11:06:47 7478-01-FH02-FIK-16-06144.jpg UniSZA Private Access A new modification of nonlinear conjugate gradient formula Far East Journal of Mathematical Sciences Nonlinear conjugate gradient (CG) methods are widely used for solving large-scale unconstrained optimization problems. Many works have tried to improve this method. It requires simplicity and low memory in numerical computation. The exact line search is used for analyzing and implementing CG methods. In this paper, a class of conjugate gradient methods possessing global convergence properties is presented. The global convergence and sufficient descent property are established using exact line searches. Numerical result demonstrated that the new formula of conjugate gradient method is superior and robust as compared to other CG coefficients. 99 4 Pushpa Publishing House Pushpa Publishing House 509-523 [1] M. R. Hestenes and E. Stiefel, Method of conjugate gradient for solving linear equations, J. Res. Nat. Bur. Stand. 49 (1952), 409-436. [2] A. Al-Baali, Descent property and global convergence of the Fletcher-Reeves method with inexact line search, IMA J. Numer. Anal. 5 (1985), 121-124. [3] Y. Dai and Y. Yuan, Nonlinear Conjugate Gradient Methods, Science Press of Shanghai, Shanghai, 2000. [4] Y. H. Dai and Y. Yuan, A nonlinear conjugate gradient method with a strong global convergent property, SIAM J. Optim. 10 (1999), 177-182. [5] Zhen-Jun Shi and Jinhua Gua, A new family of conjugate gradient methods, J. Comput. Appl. Math. 224 (2009), 444-457. [6] J. C. Gilbert and J. Nocedal, Convergence properties of conjugate gradient methods for optimization, SIAM. J. Optim. 2(1) (1992), 21-42. [7] M. J. D. Powell, Restart procedure for the conjugate gradient method, Math. Prog. 2 (1977), 241-254. [8] M. J. D. Powell, Non-convex minimization calculation and the conjugate gradient method, Lecture Notes in Mathematics, 1066, Springer-Verlag, Berlin, 1984. [9] N. Andrei, An unconstrained optimization test functions collection, Adv. Modell. Optim. 10 (2008), 147-161. [10] G. Zoutendijk, Nonlinear Programming Computational Methods, J. Abadie, ed., Integer and Nonlinear Programming, North Holland, Amsterdam, 1970, pp. 37-86. [11] W. W. Hager and H. Zhang, A new conjugate gradient method with guaranteed descent and an efficient line search, SIAM. Optim. 16 (2005), 170-192. [12] Y. H. Dai and Y. X. Yuan, A nonlinear conjugate gradient with a strong global convergence properties, SIAM J. Optim. 10 (2000), 177-182. [13] L. Zhang, W. J. Zhou and D. H. Li, Global convergence of a modified FletcherReeves conjugate method with Armijo-type line search, Numer. Math. 104 (2006), 561-572. [14] N. Andrei, A modified Polak-Ribiere-Polyak conjugate gradient algorithm for unconstrained optimization, Optimization 60 (2011), 1457-1471. [15] L. Grippo and S. Lucidi, A globally convergent version of the Polak-Ribiere gradient method, Math. Program. 78 (1997), 375-391. [16] M. Rivaie, M. Mamat, L. Wah June and M. Ismail, A new class of nonlinear conjugate gradient coefficients with global convergence properties, Appl. Math. Comput. 218 (2012), 1132-1133. [17] R. Fletcher and C. Reeves, Function minimization by conjugate gradients, Comput. J. 7 (1964), 149-154. [18] M. J. D. Powell, Non-convex minimization calculations and the conjugate gradient method, Lecture Notes in Mathematics, 1066, Springer-Verlag, Berlin, 1984. [19] E. Polak and G. Ribiere, Note Sur la convergence de directions conjugees, Rev. Francaise in Format Recherche Operationelle 3e Annee 16 (1969), 35-43. [20] Li Zhang, An improved Wei-Yao-Liu nonlinear conjugate gradient method for optimization computation, Appl. Math. Comput. 215 (2009), 2269-2274. [21] K. E. Hilstrom, A simulation test approach to the evaluation of nonlinear optimization algorithms, ACM. Trans. Math. Softw. 3 (1977), 305-315. [22] E. Dolan and J. J. More, Benchmarking optimization software with performance profile, Math. Program. 91 (2002), 201-213. [23] Z. Wei, G. Li and L. Qi, New nonlinear conjugate gradient formulas for large-scale unconstrained optimization problems, Appl. Math. Comput. 179 (2006), 407-430. [24] R. Fletcher, Practical Method of Optimization, 2nd ed., Unconstrained Optimization, Vol. I, Wiley, New York, 1997. [25] Y. Liu and C. Storey, Efficient generalized conjugate gradient algorithms. Part 1: Theory, J. Optim. Theory Appl. 69 (1992), 129-137. [26] B. T. Polyak, The conjugate gradient method in extreme problems, USSR Comput. Math. Math. Phys. 9 (1969), 94-112. [27] N. Andrei, 40 conjugate gradient algorithms for unconstrained optimization, Bull. Malay. Math. Sci. Soc. 34 (2011), 319-330.
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| spellingShingle |
A new modification of nonlinear conjugate gradient formula
|
| summary |
Nonlinear conjugate gradient (CG) methods are widely used for solving large-scale unconstrained optimization problems. Many works have tried to improve this method. It requires simplicity and low memory in numerical computation. The exact line search is used for analyzing and implementing CG methods. In this paper, a class of conjugate gradient methods possessing global convergence properties is presented. The global convergence and sufficient descent property are established using exact line searches. Numerical result demonstrated that the new formula of conjugate gradient method is superior and robust as compared to other CG coefficients.
|
| title |
A new modification of nonlinear conjugate gradient formula
|
| title_full |
A new modification of nonlinear conjugate gradient formula
|
| title_fullStr |
A new modification of nonlinear conjugate gradient formula
|
| title_full_unstemmed |
A new modification of nonlinear conjugate gradient formula
|
| title_short |
A new modification of nonlinear conjugate gradient formula
|
| title_sort |
new modification of nonlinear conjugate gradient formula
|