Parameterized Three-Term Conjugate Gradient Method

Yıl 2020, Cilt: 3 Sayı: 1, 1 - 11, 17.09.2020

Khalil Abbo Nehal H. Hameed

Öz

In this paper a new parameterized three-term conjugate gradient algorithm is suggested, the descent property and global convergence are proved for the new suggested method. Numerical experiments are employed to demonstrate the efficiency of the algorithm for solving large scale benchmark test problems, particularly in comparison with the existent state of the art algorithms available in the literature.

Anahtar Kelimeler

Conjugate Gradient

Kaynakça

• [1] M. Al-Baali, Descent property and global convergence of the Fletcher Reeves method with inexact line search, IMA J. Numer. Anal., 5(1) 1985, 121-124.
• [2] N. Andrei, New Hybrid Conjugate Gradient Algorithms for Unconstrained Optimization . In: Floudas C., Pardalos P. (eds) Encyclopedia of Optimization, Springer, Boston, 2008, 2560-2571.
• [3] N. Andrei, An unconstrained optimization test functions collection, Adv. Model. Optim, 10(1) 2008, 147-161.
• [4] I. Bongartz, A. Conn, N. Gould and P. Toint, Constrained and unconstrained testing envi-ronment, J. Optim. Theory Appl., 21(1) 1993, 123-160.
• [5] Y. Dai, Y. Yuan, A nonlinear conjugate gradient method with a strong global convergence property, SIAM J. Optimiz., 10(1) 1999, 177-182.
• [6] L. C.W. Dixon, Nonlinear optimization: A survey of the state of the art, Hatfield Polytechnic. Numerical Optimization Centre, 1973.
• [7] D. Dolan, J. Mor´e, Benchmarking optimization software with performance profiles, Math. Program., 91(2) 2002, 201-213.
• [8] K. Edwin, H. Stanilow, An introduction to optimization, Second Edition, Wiley and Sons, 2001.
• [9] R. Fletcher, C. M. Reeves, Function minimization by Conjugate gradients, Comput. J., 7(2) 1964, 149-154.
• [10] W. Hager, H. Zhang, A survey of nonlinear conjugate gradient methods, Pac. J. Optim., 2(1), 2006, 35-58.
• [11] M. Hestenes, E. Stiefel, Methods of conjugate gradients for solving linear systems, J. Res. Nat. Bur. Stand., 49(1) 1952.
• [12] K. K. Abbo, L. A. Abdulwahid, Generalized Dai-Yuan non-linear conjugate gradient method for unconstrained optimization, Int. J. Sci. Math. Educ., 8(6) 2017, 17993-17999.
• [13] X. Li, X. Zhao, A hybrid conjugate gradient method for optimization problems, Nat. Sci., 3(1) 2011, 85.
• [14] Y. Liu, C. Storey, Efficient generalized conjugate gradient algorithms, part 1: theory, J. Optimiz. Theory App., 69(1) 1991, 129-137.
• [15] J. Nocedal, J. Wright, Numerical Optimization, Springer Series in Operations Research, Springer Verlag, New York, 2006.
• [16] E. Polak and G. Ribiere, Note sur la convergence de m´ethodes de directions conjugu´ees, Rev. Fr. Inform. Rech. O., 3(16) 1969, 35-43.
• [17] S. S. Djordjevi, New hybrid conjugate gradient method as a convex combination of FR and PRP Methods. Filomat, 30(11) 2016, 3083-3100.
• [18] P. Wolfe, Convergence conditions for ascent methods, SIAM Rev., 11(2) 1969, 226-235.