The Convergence Properties of a New Kind of Conjugate Gradient Method for Unconstrained Optimization
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| internalnotes | [1] A. Abashar, M. Mamat, M. Rivaie and I. Mohd. Global convergence properties of a new class of conjugate gradient method for unconstrained optimization, Appl. Math. Sci.8 (2014), 3307-3319. http://dx.doi.org/10.12988/ams.2014.43246 [2] B. T. Polyak, The conjugate gradient method in extremal 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, Globally convergent hybrid conjugate gradient methods, J. Optim. Theory Appl. 64 (1990), 379-397. [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] G. Zoutendijk, Nonlinear programming computational methods, in: J. Abadie, (Ed.), Integer and Nonlinear Programming, North-Holland, Amsterdam, 1970, 37- 86. [6] J. C. Gilbert, 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 [7] L. Zhang, An improved Wei–Yao–Liu nonlinear conjugate gradient method for optimization computation, Appl. Math. Comput. 215(2009), 2269–2274. http://dx.doi.org/10.1016/j.amc.2009.08.016 [8] 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 [9] M.J.D. Powell, Restart procedures for the conjugate gradient method, Math. Program. 12(1977), 241-254. http://dx.doi.org/10.1007/bf01593790 [10] M.J.D. Powell, Nonconvex minimization calculations and the conjugate gradient method in Lecture notes in mathematics, 1066, Springer-Verlag, Berlin, (1984), 122–141. http://dx.doi.org/10.1007/bfb0099521 [11] M. R. Hestenes and E. L. Stiefel, Methods of conjugate gradients for solving linear systems, J. Research Nat. Bur. Standards, 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, Appl. Math. Comput. 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, Applied Mathematical Sciences, 8 (2014), 33-44. http://dx.doi.org/10.12988/ams.2014.310578 [14] M. Rivaie, M. Mamat, M. Ismail and M. Fauzi, A comparative study of conjugate gradient coefficient for unconstrained optimization, Aus. J. Bas. Appl. Sci. 5 (2011), 947-951. [15] N. Andrei, An unconstrained optimization test functions collection, Adv. Modell. Optim. 10 (2008), 147-161. [16] R. Fletcher, C. Reeves, Function minimization by conjugate gradients, Comput. J. 7 (1964), 149-154. http://dx.doi.org/10.1093/comjnl/7.2.149 [17] R. Fletcher, Practical Method of Optimization, Vol. 1, Unconstrained Optimization, Vol.I, Wiley, New York, 1987. [18] 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 [19] W. W. Hager and H.C. Zhang, A survey of nonlinear conjugate gradient methods, Pacific Journal of Optimization 2(1), (2006), 335-58. [20] Y. Liu, and C. Storey, Efficient generalized conjugate gradient algorithms. Part 1: Theory, J. Optim. Theory Appl. 69 (1991), 129–137. http://dx.doi.org/10.1007/bf00940464 [21] Y.H. Dai, and Y. Yuan, A nonlinear conjugate gradient method with a strong global convergence property, SIAM J. Optim. 10 (2000), 177–182. http://dx.doi.org/10.1137/s1052623497318992 [22] Z. Wei, S. Yao and L. Liu, 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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| spelling | 12078 https://intelek.unisza.edu.my/intelek/pages/view.php?ref=12078 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 User user USER UsEr 2024-08-26 18:14:17 6381-01-FH02-FIK-15-03352.pdf UniSZA Private Access The Convergence Properties of a New Kind of Conjugate Gradient Method for Unconstrained Optimization Applied Mathematical Sciences Conjugate gradient (CG) methods are the most prominent technique for solving large-scale unconstrained optimization problems, due to its robustness, low memory requirement, and global convergence properties. Numerous studies and modifications have been carried out recently to improve these methods. In this paper, a new modification of a CG coefficient that possesses the global convergence properties is presented. The global convergence result is validated using exact line search. Several numerical experiments showed that, the proposed formula is found to be robust and efficient when compared to other CG coefficients. 9 38 HIKARI Ltd. HIKARI Ltd. 1845-1856 [1] A. Abashar, M. Mamat, M. Rivaie and I. Mohd. Global convergence properties of a new class of conjugate gradient method for unconstrained optimization, Appl. Math. Sci.8 (2014), 3307-3319. http://dx.doi.org/10.12988/ams.2014.43246 [2] B. T. Polyak, The conjugate gradient method in extremal 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, Globally convergent hybrid conjugate gradient methods, J. Optim. Theory Appl. 64 (1990), 379-397. [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] G. Zoutendijk, Nonlinear programming computational methods, in: J. Abadie, (Ed.), Integer and Nonlinear Programming, North-Holland, Amsterdam, 1970, 37- 86. [6] J. C. Gilbert, 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 [7] L. Zhang, An improved Wei–Yao–Liu nonlinear conjugate gradient method for optimization computation, Appl. Math. Comput. 215(2009), 2269–2274. http://dx.doi.org/10.1016/j.amc.2009.08.016 [8] 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 [9] M.J.D. Powell, Restart procedures for the conjugate gradient method, Math. Program. 12(1977), 241-254. http://dx.doi.org/10.1007/bf01593790 [10] M.J.D. Powell, Nonconvex minimization calculations and the conjugate gradient method in Lecture notes in mathematics, 1066, Springer-Verlag, Berlin, (1984), 122–141. http://dx.doi.org/10.1007/bfb0099521 [11] M. R. Hestenes and E. L. Stiefel, Methods of conjugate gradients for solving linear systems, J. Research Nat. Bur. Standards, 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, Appl. Math. Comput. 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, Applied Mathematical Sciences, 8 (2014), 33-44. http://dx.doi.org/10.12988/ams.2014.310578 [14] M. Rivaie, M. Mamat, M. Ismail and M. Fauzi, A comparative study of conjugate gradient coefficient for unconstrained optimization, Aus. J. Bas. Appl. Sci. 5 (2011), 947-951. [15] N. Andrei, An unconstrained optimization test functions collection, Adv. Modell. Optim. 10 (2008), 147-161. [16] R. Fletcher, C. Reeves, Function minimization by conjugate gradients, Comput. J. 7 (1964), 149-154. http://dx.doi.org/10.1093/comjnl/7.2.149 [17] R. Fletcher, Practical Method of Optimization, Vol. 1, Unconstrained Optimization, Vol.I, Wiley, New York, 1987. [18] 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 [19] W. W. Hager and H.C. Zhang, A survey of nonlinear conjugate gradient methods, Pacific Journal of Optimization 2(1), (2006), 335-58. [20] Y. Liu, and C. Storey, Efficient generalized conjugate gradient algorithms. Part 1: Theory, J. Optim. Theory Appl. 69 (1991), 129–137. http://dx.doi.org/10.1007/bf00940464 [21] Y.H. Dai, and Y. Yuan, A nonlinear conjugate gradient method with a strong global convergence property, SIAM J. Optim. 10 (2000), 177–182. http://dx.doi.org/10.1137/s1052623497318992 [22] Z. Wei, S. Yao and L. Liu, 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 | The Convergence Properties of a New Kind of Conjugate Gradient Method for Unconstrained Optimization |
| summary | Conjugate gradient (CG) methods are the most prominent technique for solving large-scale unconstrained optimization problems, due to its robustness, low memory requirement, and global convergence properties. Numerous studies and modifications have been carried out recently to improve these methods. In this paper, a new modification of a CG coefficient that possesses the global convergence properties is presented. The global convergence result is validated using exact line search. Several numerical experiments showed that, the proposed formula is found to be robust and efficient when compared to other CG coefficients. |
| title | The Convergence Properties of a New Kind of Conjugate Gradient Method for Unconstrained Optimization |
| title_full | The Convergence Properties of a New Kind of Conjugate Gradient Method for Unconstrained Optimization |
| title_fullStr | The Convergence Properties of a New Kind of Conjugate Gradient Method for Unconstrained Optimization |
| title_full_unstemmed | The Convergence Properties of a New Kind of Conjugate Gradient Method for Unconstrained Optimization |
| title_short | The Convergence Properties of a New Kind of Conjugate Gradient Method for Unconstrained Optimization |
| title_sort | convergence properties of a new kind of conjugate gradient method for unconstrained optimization |