Globally convergence of nonlinear conjugate gradient method for unconstrained optimization
Sellami, B.1 ; Belloufi, M.1 ; Chaib, Y.1
1 Department of mathematics and informatics, Mohamed Cherif Messaadia University, Souk-Ahras, Algeria.
RAIRO - Operations Research - Recherche Opérationnelle, Tome 51 (2017) no. 4, pp. 1101-1117.

The conjugate gradient method is a useful and powerful approach for solving large-scale minimization problems. In this paper, a new nonlinear conjugate gradient method is proposed for large-scale unconstrained optimization. This method include the already existing two practical nonlinear conjugate gradient methods, to combine the nice global convergence properties of Fletcher-Reeves method (abbreviated FR) and the good numerical performances of the Polak–Ribiére–Polyak method (abbreviated PRP), which produces a descent search direction at every iteration and converges globally provided that the line search satisfies the Wolfe conditions. Our numerical results show that of the new method is very efficient for the given test problems. In addition we will study the methods related to the new nonlinear conjugate gradient method.

DOI : 10.1051/ro/2017028
Classification : 65K05, 90C25, 90C26, 90C27, 90C30
Mots-clés : Unconstrained optimization, conjugate gradient method, line search, global convergence
Sellami, B. 1 ; Belloufi, M. 1 ; Chaib, Y. 1

1 Department of mathematics and informatics, Mohamed Cherif Messaadia University, Souk-Ahras, Algeria. 
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     title = {Globally convergence of nonlinear conjugate gradient method for unconstrained optimization},
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Sellami, B.; Belloufi, M.; Chaib, Y. Globally convergence of nonlinear conjugate gradient method for unconstrained optimization. RAIRO - Operations Research - Recherche Opérationnelle, Tome 51 (2017) no. 4, pp. 1101-1117. doi : 10.1051/ro/2017028. http://www.numdam.org/articles/10.1051/ro/2017028/

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