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1860796950284075008
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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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2024-10-02 15:24
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Restricted Document
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10800
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UniSZA
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[1] B.T. Polyak, The conjugate gradient method in extreme problems, USSR Comp .Math. Phys. 9 (1969), 94–112. [2] D. Touati-Ahmed, C. Storey, Globally convergent hybrid conjugate gradient methods, J. Optim. Theory Appl. 64 (1990), 379–397. [3] E.Dolan, J.J. More, Benchmarking optimization software with performance profile, Math. Prog. 91 (2002), 201–213. [4] G. Zoutendijk, Nonlinear programming computational methods, in: J. Abadie (Ed.), Integer and Nonlinear Programming, North-Holland, Amsterdam, 1970, pp. 37–86. [5] G. Yuan, X. Lu, Z. Wei, A conjugate gradient method with descent direction for unconstrained optimization, J. Comput. Appl. Math. 233 (2009), 519– 530. [6] J.C. Gilbert, J. Nocedal, Global convergence properties of conjugate gradient methods for optimization, SIAM J. Optim.2 (1992), 21– 42. [7] K.E. Hilstrom, A simulation test approach to the evaluation of nonlinear optimization algorithms, ACM. Trans. Math. Softw. 3 (1977), 305–315. [8] M.R. Hestenes, E. Stiefel, Method of conjugate gradient for solving linear equations, J. Res. Nat. Bur. Stand. 49 (1952), 409–436. [9] M. Al-Baali, Descent property and global convergence of Fletcher-Reeves method with inexact line search, IMA. J. Numer. Anal. 5 (1985), 121–124. [10] M.J.D. Powell, Non-convex minimization calculation and the conjugate gradient method, Lecture Notes in Mathematics, 1066, Springer-Verlag, Berlin, 1984, pp. 122–241. [11] M. Rivaie, M. Mamat, W.J. Leong, M. Ismail, A new class of nonlinear conjugate gradient coefficients with global convergence properties. Appl. Math. comput. 218 (2012) ,11323-11332. [12] N. Andrei, An unconstrained optimization test functions collection, Adv. Modell. Optim. 10 (2008), 147–161. [13] R. Fletcher, C. Reeves, Function minimization by conjugate gradients, Compute. J. 7 (1964), 149–154. [14] R. Fletcher, Practical Method of Optimization, second ed., Unconstrained Optimization, vol. I, Wiley,New York, 1997. [15] W.W. Hager, H.C. Zhang, A new conjugate gradient method with guaranteed descent and efficient line search, SIAM J. Optim. 16 (2005), 170–192. [16] Y. Dai, Y. Yuan, A nonlinear conjugate gradient with strong global convergence properties, SIAM J. Optim. 10 (2000), 177–182. [17] Y. Liu, C. Storey, Efficient generalized conjugate gradient algorithms, part 1: theory, J. Optim. Theory Appl. 69 (1992), 129–137.
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10800 https://intelek.unisza.edu.my/intelek/pages/view.php?ref=10800 https://intelek.unisza.edu.my/intelek/pages/search.php?search=!collection407072 Restricted Document Article Journal image/jpeg inches 96 96 2024-10-02 15:24 626 1341x626 1341 4931-01-FH02-FIK-14-00725.jpg UniSZA Private Access The convergence properties of a new type of conjugate gradient methods Applied Mathematical Sciences Conjugate gradient (CG) methods are widely used for solving large scale unconstrained optimization problems. Many studies have been devoted to develop and improve these methods. In this paper, we compare our new CG coefficient ( k) with the other classical formulas of CG methods under the exact line search. Numerical results have shown that our new k performs better than these classical formulas. Our method also possesses global convergence properties. 8 1 33-44 [1] B.T. Polyak, The conjugate gradient method in extreme problems, USSR Comp .Math. Phys. 9 (1969), 94–112. [2] D. Touati-Ahmed, C. Storey, Globally convergent hybrid conjugate gradient methods, J. Optim. Theory Appl. 64 (1990), 379–397. [3] E.Dolan, J.J. More, Benchmarking optimization software with performance profile, Math. Prog. 91 (2002), 201–213. [4] G. Zoutendijk, Nonlinear programming computational methods, in: J. Abadie (Ed.), Integer and Nonlinear Programming, North-Holland, Amsterdam, 1970, pp. 37–86. [5] G. Yuan, X. Lu, Z. Wei, A conjugate gradient method with descent direction for unconstrained optimization, J. Comput. Appl. Math. 233 (2009), 519– 530. [6] J.C. Gilbert, J. Nocedal, Global convergence properties of conjugate gradient methods for optimization, SIAM J. Optim.2 (1992), 21– 42. [7] K.E. Hilstrom, A simulation test approach to the evaluation of nonlinear optimization algorithms, ACM. Trans. Math. Softw. 3 (1977), 305–315. [8] M.R. Hestenes, E. Stiefel, Method of conjugate gradient for solving linear equations, J. Res. Nat. Bur. Stand. 49 (1952), 409–436. [9] M. Al-Baali, Descent property and global convergence of Fletcher-Reeves method with inexact line search, IMA. J. Numer. Anal. 5 (1985), 121–124. [10] M.J.D. Powell, Non-convex minimization calculation and the conjugate gradient method, Lecture Notes in Mathematics, 1066, Springer-Verlag, Berlin, 1984, pp. 122–241. [11] M. Rivaie, M. Mamat, W.J. Leong, M. Ismail, A new class of nonlinear conjugate gradient coefficients with global convergence properties. Appl. Math. comput. 218 (2012) ,11323-11332. [12] N. Andrei, An unconstrained optimization test functions collection, Adv. Modell. Optim. 10 (2008), 147–161. [13] R. Fletcher, C. Reeves, Function minimization by conjugate gradients, Compute. J. 7 (1964), 149–154. [14] R. Fletcher, Practical Method of Optimization, second ed., Unconstrained Optimization, vol. I, Wiley,New York, 1997. [15] W.W. Hager, H.C. Zhang, A new conjugate gradient method with guaranteed descent and efficient line search, SIAM J. Optim. 16 (2005), 170–192. [16] Y. Dai, Y. Yuan, A nonlinear conjugate gradient with strong global convergence properties, SIAM J. Optim. 10 (2000), 177–182. [17] Y. Liu, C. Storey, Efficient generalized conjugate gradient algorithms, part 1: theory, J. Optim. Theory Appl. 69 (1992), 129–137.
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| spellingShingle |
The convergence properties of a new type of conjugate gradient methods
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| summary |
Conjugate gradient (CG) methods are widely used for solving large scale unconstrained optimization problems. Many studies have been devoted to develop and improve these methods. In this paper, we compare our new CG coefficient ( k) with the other classical formulas of CG methods under the exact line search. Numerical results have shown that our new k performs better than these classical formulas. Our method also possesses global convergence properties.
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| title |
The convergence properties of a new type of conjugate gradient methods
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| title_full |
The convergence properties of a new type of conjugate gradient methods
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| title_fullStr |
The convergence properties of a new type of conjugate gradient methods
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| title_full_unstemmed |
The convergence properties of a new type of conjugate gradient methods
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| title_short |
The convergence properties of a new type of conjugate gradient methods
|
| title_sort |
convergence properties of a new type of conjugate gradient methods
|