A New effected Three-Term Hestenes-Stiefel Conjugate-Gradient Method for Solving Unconstrained Optimization Problems
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Abstract
In this paper 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.
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References
[1] Al-Bayati, A. and Hassan, B. (2006), Some
Theoretical Results for Oren Variable Metric Method.
J. of Kirkuk University, Iraq, 1, 26-31.
[2] Andrei, N. (2013), A simple three-term conjugate
gradient algorithm for unconstrained optimization ,
Journal of Computational and Applied Mathematics,
241, 19–29.
[3] Dennis, J. and More, J. (1977), Quasi-Newton
methods, motivation and theory, SIAM Review, 19,
46-89.
[4] Fletcher, R. (1987), Practical Methods of
Optimization (second edition)", John Wiley and Sons,
New York.
[5] Hestenes, M. and Stiefel, E. (1952) , Method of
conjugate gradients for solving linear systems", J.
Research Nat. Standards , 49, 409-436.
[6] Nazareth, L. (1977), A conjugate direction
algorithm without line search. Journal of
Optimization Theory and Applications, 23, 373-387.
[7] Shanno, D. (1978), Conjugate gradient methods
with inexact searches, Math. of operation Research,
3, 244-256.
[8] Zhang, L. Zhou, Y. (2012), A note on the
convergence properties of the original three-term
Hestenes–Stiefel method, AMO-Advanced Modeling
and Optimization, 14, 159–163.
[9] Zhang, L. Zhou, W. and Li, D. (2007), Some
descent three-term conjugate gradient methods and
their global convergence. Optimization Methods and
Software, 22, 697- 711.
[10] Zhang, J.; Xiao, Y. and Wei, Z. (2009),
Nonlinear conjugate gradient methods with sufficient
descent condition for large-scale unconstrained
optimization. Math. Prog. Eng., Article ID 243290,
16. DOI: 10.1155/2009/243290.
[11] Bongartz, I.; Conn, A.; Gold, N. and Toint, P.
(1995), CUTE: constrained and unconstrained testing
environment, ACM Trans., Math. Software, 21.