In this paper, a new conjugate gradient method is proposed for large-scale unconstrained optimization. This method includes the already existing three practical nonlinear conjugate gradient methods, which produces a descent search direction at every iteration and converges globally provided that the line search satisfies the Wolfe conditions. The numerical experiments are done to test the efficiency of the new method, which confirms the promising potentials of the new method.
Mots clés : Unconstrained optimization, conjugate gradient method, line search, global convergence
@article{RO_2016__50_4-5_1013_0,
author = {Sellami, Badreddine and Chaib, Yacine},
title = {New conjugate gradient method for unconstrained optimization},
journal = {RAIRO - Operations Research - Recherche Op\'erationnelle},
pages = {1013--1026},
publisher = {EDP-Sciences},
volume = {50},
number = {4-5},
year = {2016},
doi = {10.1051/ro/2015064},
zbl = {1357.65076},
mrnumber = {3570546},
language = {en},
url = {http://www.numdam.org/articles/10.1051/ro/2015064/}
}
TY - JOUR AU - Sellami, Badreddine AU - Chaib, Yacine TI - New conjugate gradient method for unconstrained optimization JO - RAIRO - Operations Research - Recherche Opérationnelle PY - 2016 SP - 1013 EP - 1026 VL - 50 IS - 4-5 PB - EDP-Sciences UR - http://www.numdam.org/articles/10.1051/ro/2015064/ DO - 10.1051/ro/2015064 LA - en ID - RO_2016__50_4-5_1013_0 ER -
%0 Journal Article %A Sellami, Badreddine %A Chaib, Yacine %T New conjugate gradient method for unconstrained optimization %J RAIRO - Operations Research - Recherche Opérationnelle %D 2016 %P 1013-1026 %V 50 %N 4-5 %I EDP-Sciences %U http://www.numdam.org/articles/10.1051/ro/2015064/ %R 10.1051/ro/2015064 %G en %F RO_2016__50_4-5_1013_0
Sellami, Badreddine; Chaib, Yacine. New conjugate gradient method for unconstrained optimization. RAIRO - Operations Research - Recherche Opérationnelle, Tome 50 (2016) no. 4-5, pp. 1013-1026. doi : 10.1051/ro/2015064. http://www.numdam.org/articles/10.1051/ro/2015064/
, Descent property and global convergence of the Fletcher-Reeves method with inexact line search. IMA J. Numer. Anal. 5 (1985) 121–124. | DOI | MR | Zbl
, New property and global convergence of the Fletcher-Reeves method with inexact line searches. IMA J. Numer. Anal. 5 (1985) 122–124. | DOI | MR | Zbl
, An unconstrained optimization test functions collection. Adv. Model. Optim 10 (2008) 147–161. | MR | Zbl
, , and , Cute: Constrained and unconstrained testing environment. ACM Trans. Math. Software (TOMS) 21 (1995) 123–160. | DOI | Zbl
Y. Dai and Y. Yuan, Some properties of a new conjugate gradient method. In Advances in Nonlinear Programming. Springer (1998) 251–262. | MR | Zbl
and , A nonlinear conjugate gradient method with a strong global convergence property. SIAM J. Optim. 10 (1999) 177–182. | DOI | MR | Zbl
and , A three-parameter family of nonlinear conjugate gradient methods. Math. Comput. 70 (2001) 1155–1167. | DOI | MR | Zbl
and , A class of globally convergent conjugate gradient methods. Sci. China Ser. A: Math. 46 (2003) 251–261. | DOI | MR | Zbl
, , , , and , Convergence properties of nonlinear conjugate gradient methods. SIAM J. Optim. 10 (2000) 345–358. | DOI | MR | Zbl
and , Function minimization by conjugate gradients. Comput. J. 7 (1964) 149–154. | DOI | MR | Zbl
and , Global convergence properties of conjugate gradient methods for optimization. SIAM J. Optim. 2 (1992) 21–42. | DOI | MR | Zbl
and , A survey of nonlinear conjugate gradient methods. Pacific J. Optim. 2 (2006) 35–58. | MR | Zbl
, Methods of conjugate gradients for solving linear systems. Res. J. Natl. Bur. Stan. 49 (1952) 409–436. | DOI | MR | Zbl
and , Global convergence result for conjugate gradient methods. J. Optim. Theory Appl. 71 (1991) 399–405. | DOI | MR | Zbl
and , Benchmarking optimization software with performance files. Math. Program. 91 (2002) 201–2013. | DOI | MR | Zbl
and , Note sur la convergence de méthodes de directions conjuguées. Revue française d’informatique et de recherche opérationnelle, série rouge 3 (1969) 35–43. | Numdam | MR | Zbl
, The conjugate gradient method in extremal problems. USSR Comput. Math. Math. Phys. 9 (1969) 94–112. | DOI | Zbl
M. Powell, Nonconvex minimization calculations and the conjugate gradient method. Numer. Anal. (1984) 122–141. | MR | Zbl
, and , A new two-parameter family of nonlinear conjugate gradient methods. Optimization 64 (2015) 993–1009. | DOI | MR | Zbl
, Conjugate gradient methods with inexact searches. Math. Oper. Res. 3 (1978) 244–256. | DOI | MR | Zbl
, Convergence conditions for ascent methods. SIAM Rev. 11 (1969) 226–235. | DOI | MR | Zbl
, Convergence conditions for ascent methods. ii: Some corrections. SIAM Rev. 13 (1971) 185–188. | DOI | MR | Zbl
G. Zoutendijk, Nonlinear programming, computational methods. In Integer and Nonlinear Programming, edited by J. Abadie. North-Holland, Amsterdam (1970) 37–86. | MR | Zbl
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