پیوندهای مفید
آمار
| تعداد نشریات | 21 |
| تعداد شمارهها | 691 |
| تعداد مقالات | 10,035 |
| تعداد مشاهده مقاله | 71,039,785 |
| تعداد دریافت فایل اصل مقاله | 62,489,385 |
An improved PRP conjugate gradient method for optimization computation | ||
| International Journal of Nonlinear Analysis and Applications | ||
| مقاله 10، دوره 15، شماره 11، بهمن 2024، صفحه 139-147 اصل مقاله (1.01 M) | ||
| نوع مقاله: Research Paper | ||
| شناسه دیجیتال (DOI): 10.22075/ijnaa.2023.28524.3918 | ||
| نویسندگان | ||
| Bachir Barrouk* 1، 2؛ Mohammed Belloufi2؛ Rachid Benzine3؛ Taher Bechouat2 | ||
| 1Badji Mokhtar University, Annaba, 23000, Algeria | ||
| 2Laboratory Informatics and Mathematics (LiM), Mohamed Cherif Messaadia University, Souk Ahras, 41000, Algeria | ||
| 3Superior School of Industrial Technologies, Annaba, 23000, Algeria | ||
| تاریخ دریافت: 03 مهر 1401، تاریخ پذیرش: 05 آبان 1402 | ||
| چکیده | ||
| The conjugate gradient method plays a very important role in several fields, to solve problems of large sizes. To improve the efficiency of this method, a lot of work has been done; in this paper, we propose a new modification of PRP method to solve a large scale unconstrained optimization problems in relation with strong Wolf Powell Line Search property, when the latter was used under some conditions, a global convergence result was proved. In comparison with other known methods the efficiency of this method proved that it is better in the number of iterations and in time on $90$ proposed problems by use of Matlab. | ||
| کلیدواژهها | ||
| Unconstrained optimization؛ Conjugate gradient method؛ strong wolfe line search؛ Numerical comparisons | ||
| مراجع | ||
|
[1] M. Al-Baali, Descent property and global convergence of the Fletcher—Reeves method with inexact line search, IMA J. Numer. Anal. 5 (1985), no. 1, 121–124. [2] N. Andrei, An unconstrained optimization test functions collection, Adv. Model. Optim 10 (2008), no. 1, 147–161. [3] E. Blum, From optimization and variational inequalities to equilibrium problems, Math. Student 63 (1994), 123–145. [4] F.H. Clarke, Y.S. Ledyaev, R.J. Stern, and P.R. Wolenski, Nonsmooth Analysis and Control Theory, vol. 178, Springer Science & Business Media, 2008. [5] R. Fletcher and C.M. Reeves, Function minimization by conjugate gradients, Comput. J 7 (1964), no. 2, 149–154. [6] J.C. Gilbert and J. Nocedal, Global convergence properties of conjugate gradient methods for optimization, SIAM J. Optim. 2 (1992), no. 1, 21–42. [7] M. Hamoda, M. Mamat, M. Rivaie, and Z. Salleh, A conjugate gradient method with strong Wolfe-Powell line search for unconstrained optimization, Appl. Math. Sci. 10 (2016), 721–734. [8] M.R Hestenes and E. Stiefel, Methods of conjugate gradients for solving, J. Res. Nat. Bureau Stand. 49 (1952), no. 6, 409. [9] D.E. Knuth, The TEXbook, Addison Wesley Professional, Massachusetts, 1984. [10] G. Li, C. Tang, and Z.Wei, New conjugacy condition and related new conjugate gradient methods for unconstrained optimization, J. Comput. Appl. Math. 202 (2007), no. 2, 523–539. [11] Y. Liu and C. Storey, Efficient generalized conjugate gradient algorithms, part 1: theory, J. Optim. Theory Appl. 69 (1991), no. 1, 129–137. [12] Mu. Mamat, M. Rivaie, I. Mohd, and M. Fauzi, A new conjugate gradient coefficient for unconstrained optimization, Int. J. Contemp. Math. Sci. 5 (2010), no. 29, 1429–1437. [13] I.S. Mohammed, M. Mamat, A. Abashar, M. Rivaie, and Z. Salleh, A modified nonlinear conjugate gradient method for unconstrained optimization, Appl. Math. Sci. 9 (2015), no. 54, 2671–2682. [14] T. Nguyen Xuan and T. Phan Nhat, On the existence of equilibrium points of vector functions, Numer. Funct. Anal. Optim. 19 (1998), no. 1-2, 141–156. [15] O. Omer, M. Mamat, and M. Rivaie, The global convergence properties of a family of conjugate gradient method under the strong Wolfe line search, Abstr. Appl. Anal., vol. 2015, 2015. [16] M.J.D. Powell, Restart procedures for the conjugate gradient method, Math. Program. 12 (1977), no. 1, 241–254. [17] G. Quon, S. Haider, A.G. Deshwar, A. Cui, P.C. Boutros, and Q. Morris, Computational purification of individual tumor gene expression profiles leads to significant improvements in prognostic prediction, Genome Med. 5 (2013), no. 3, 1–20. [18] 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. [19] M. Rivaie, M. Mamat, L.W. June, and I. Mohd, A new class of nonlinear conjugate gradient coefficients with global convergence properties, Appl. Math. Comput. 218 (2012), no. 22, 11323–11332. [20] D. Touati-Ahmed and C. Storey, Efficient hybrid conjugate gradient techniques, J. Optim. Theory Appl. 64 (1990), no. 2, 379–397. [21] X. Wang, and J. Chi, Cg global convergence properties with Goldstein line search, Bull. Brazil. Math. Soc. 36 (2005), no. 2, 197–204. [22] Z. Wei and L. Li, and G. Qi, New nonlinear conjugate gradient formulas for large-scale unconstrained optimization problems, Appl. Math. Comput. 179 (2006), no. 2, 407–430. [23] Z. Wei, S. Yao, and L. Liu, The convergence properties of some new conjugate gradient methods, Appl. Math. Comput. 183 (2006), no. 2, 1341–1350. | ||
|
آمار تعداد مشاهده مقاله: 1,527 تعداد دریافت فایل اصل مقاله: 961 |
||