| _version_ |
1860797249993310208
|
| building |
INTELEK Repository
|
| collection |
Online Access
|
| collectionurl |
https://intelek.unisza.edu.my/intelek/pages/search.php?search=!collection407072
|
| date |
2024-08-26 17:53:43
|
| format |
Restricted Document
|
| id |
11948
|
| institution |
UniSZA
|
| internalnotes |
[1] Abashar, A., Mamat, M., Rivaie, M., and Mohd, I. Global convergence properties of a new class of conjugate gradient method for unconstrained optimization, Applied Mathematical Science. 8(2014), 3307-3319. http://dx.doi.org/10.12988/ams.2014.43246 [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. Zoutendijk, Nonlinear programming, computational methods, in Integer and Nonlinear Programming, J. Abadie, ed., North- Holland, Amsterdam, (1970), 37-86. [7] Jusoh, I., Mamat, M., and Rivaie, M. A new edition of conjugate gradient methods for large-scale unconstrained optimization, Intl. J. Math. Anal. 8 (2014), 2277-2291. http://dx.doi.org/10.12988/ijma.2014.44115 [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] 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 [10] M. J. D. Powell, Convergence properties of algorithm for nonlinear optimization, SIAM Rev. 28 (1986), 487-500. http://dx.doi.org/10.1137/1028154 [11] 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 [12] 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 [13] M. Rivaie, A. Abashar, M. Mamat and I. Mohd, The convergence properties of a new type of conjugate gradient methods, Appl. Math. Sci .8 (2014), 33-44. http://dx.doi.org/10.12988/ams.2014.310578 [14] N. Andrei, An unconstrained optimization test functions collection, Advanced Modelling and Optimization 10(1) (2008), 147-161. [15] 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 [16] R. Fletcher, Practical Method of Optimization, Vol. 1, Unconstrained Optimization, John Wiley & Sons, New York, 1987. [17] 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 [18] Sofi, A. Z. M., Mamat, M., and Mohd, I. An improved BFGS search direction using exact line search for solving unconstrained optimization problems. Applied Mathematical Science. 7 (2013), 73-85. [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. http://dx.doi.org/10.1137/030601880 [20] Y. H. Dai, Y. Yuan, A nonlinear conjugate gradient with a strong global convergence properties, SIAM J. Optim. 10 (1999), 177-182. http://dx.doi.org/10.1137/s1052623497318992 [21] Y. Liu, 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 [22] 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
|
| originalfilename |
6249-01-FH02-FIK-15-03341.pdf
|
| person |
win7
Win7
|
| recordtype |
oai_dc
|
| resourceurl |
https://intelek.unisza.edu.my/intelek/pages/view.php?ref=11948
|
| spelling |
11948 https://intelek.unisza.edu.my/intelek/pages/view.php?ref=11948 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 17:53:43 6249-01-FH02-FIK-15-03341.pdf UniSZA Private Access A Modified Nonlinear Conjugate Gradient Method for Unconstrained Optimization Applied Mathematical Sciences Nonlinear conjugate gradient method holds an important role in solving large scale unconstrained optimization problems. Their simplicity, low memory requirement, and global convergence stimulated a massive study on the method. Numerous modifications have been done recently to improve its performance. In this paper, we proposed a new formula for the conjugate gradient coefficient k that generates the descent search direction. In addition, we establish the global convergence result under exact line search. The outcome of our numerical experiment show that the proposed formula is very efficient and more reliable when compare to other conjugate gradient methods. 9 54 HIKARI Ltd. HIKARI Ltd. 2671-2682 [1] Abashar, A., Mamat, M., Rivaie, M., and Mohd, I. Global convergence properties of a new class of conjugate gradient method for unconstrained optimization, Applied Mathematical Science. 8(2014), 3307-3319. http://dx.doi.org/10.12988/ams.2014.43246 [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. Zoutendijk, Nonlinear programming, computational methods, in Integer and Nonlinear Programming, J. Abadie, ed., North- Holland, Amsterdam, (1970), 37-86. [7] Jusoh, I., Mamat, M., and Rivaie, M. A new edition of conjugate gradient methods for large-scale unconstrained optimization, Intl. J. Math. Anal. 8 (2014), 2277-2291. http://dx.doi.org/10.12988/ijma.2014.44115 [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] 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 [10] M. J. D. Powell, Convergence properties of algorithm for nonlinear optimization, SIAM Rev. 28 (1986), 487-500. http://dx.doi.org/10.1137/1028154 [11] 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 [12] 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 [13] M. Rivaie, A. Abashar, M. Mamat and I. Mohd, The convergence properties of a new type of conjugate gradient methods, Appl. Math. Sci .8 (2014), 33-44. http://dx.doi.org/10.12988/ams.2014.310578 [14] N. Andrei, An unconstrained optimization test functions collection, Advanced Modelling and Optimization 10(1) (2008), 147-161. [15] 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 [16] R. Fletcher, Practical Method of Optimization, Vol. 1, Unconstrained Optimization, John Wiley & Sons, New York, 1987. [17] 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 [18] Sofi, A. Z. M., Mamat, M., and Mohd, I. An improved BFGS search direction using exact line search for solving unconstrained optimization problems. Applied Mathematical Science. 7 (2013), 73-85. [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. http://dx.doi.org/10.1137/030601880 [20] Y. H. Dai, Y. Yuan, A nonlinear conjugate gradient with a strong global convergence properties, SIAM J. Optim. 10 (1999), 177-182. http://dx.doi.org/10.1137/s1052623497318992 [21] Y. Liu, 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 [22] 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
|
| spellingShingle |
A Modified Nonlinear Conjugate Gradient Method for Unconstrained Optimization
|
| summary |
Nonlinear conjugate gradient method holds an important role in solving large scale unconstrained optimization problems. Their simplicity, low memory requirement, and global convergence stimulated a massive study on the method. Numerous modifications have been done recently to improve its performance. In this paper, we proposed a new formula for the conjugate gradient coefficient k that generates the descent search direction. In addition, we establish the global convergence result under exact line search. The outcome of our numerical experiment show that the proposed formula is very efficient and more reliable when compare to other conjugate gradient methods.
|
| title |
A Modified Nonlinear Conjugate Gradient Method for Unconstrained Optimization
|
| title_full |
A Modified Nonlinear Conjugate Gradient Method for Unconstrained Optimization
|
| title_fullStr |
A Modified Nonlinear Conjugate Gradient Method for Unconstrained Optimization
|
| title_full_unstemmed |
A Modified Nonlinear Conjugate Gradient Method for Unconstrained Optimization
|
| title_short |
A Modified Nonlinear Conjugate Gradient Method for Unconstrained Optimization
|
| title_sort |
modified nonlinear conjugate gradient method for unconstrained optimization
|