Three-Term Conjugate Gradient Algorithm For Solve Unconstrained Optimization Problems

Yıl 2018, Cilt: 1 Sayı: 2, 82 - 90, 21.01.2019

Khalil Abbo Hassan . Ibrahim İsam Albayaty

Öz

In this paper, we Proposed  a new
three–term Conjugate Gradient (CG) method is suggested, the derivation of the
method based on the descent property and conjugacy condition, the global
convergence property is analyzed; numerical results indicate that the new
proposed CG-method is well compared against other similar CG-methods in this
field.

Anahtar Kelimeler

Three-term conjugate gradient, Descent property, Conjugacy condition

Kaynakça

• [1]] N. Andrei, An unconstrained optimization test function collection, Adv. Model. Optim., 10(1) 2008, 147-161.[2] N. Andrei, A simple three-term conjugate gradient algorithm for unconstrained optimiza-tion, J. Comput. Appl. Math., (241) 2013, 19–29.[3] I. Bongartz, A. Conn, N. Gould and P. Toint, Constrained and unconstrained testing envi-ronment, J. Optim. Theory Appl., 21(1), 1993, 123–160 [4] J. Dennis and J. More, Quasi-Newton methods, motivation and theory, SIAM Rev., 19(1) 1977, 46-89.[5] D. Dolan and J. Moré, Benchmarking optimization software with performance profiles, Math. Program., 91(2) 2002, 201-213.[6] R. Fletcher, Practical Methods of Optimization (second edition), John Wiley and Sons, New York, 1987.[7]M. Hestenes and E. Stiefel, Methods of conjugate Gradients For solving linear systems, J. Res. Nat. Bur. Stand., 49(1) 1952.[8] L. Nazareth, A conjugate direction algorithm without line search, J. Optimiz. Theory App., 23(3) 1977, 373-387. [9] D. Shanno, Conjugate gradient methods with inexact searches, Math. Oper. Res., 3(3) 1978, 244-256.[10] J. Zhang, Y. Xiao and Z. Wei, Nonlinear conjugate gradient methods with sufficient de-scent condition for large-scale unconstrained optimization. Math. Probl. Eng., 2009. Doi: 10.1155/2009/243290.[11] L. Zhang and Y. Zhou, A note on the convergence properties of the original three-term Hestenes–Stiefel method, AMO-Advanced Modeling and Optimization, (14) 2012, 159–163. [12] L. Zhang, W. Zhou and D. Li, Some descent three-term conjugate gradient methods and their global convergence, Optim. Method Softw., 22(4) 2007, 697- 711. [13] I. H. Albayaty, New Version Of The Three-Term Conjugate Gradient Method For Solve Unconstrained Optimization, 2017. Doi:10.24327/ijrsr.2017.0805.0268