Hybridizing self-adjusting approach of Dong et al. and three-term formulation of Zhang et al., a nonlinear conjugate gradient method is proposed. The method reduces to the Polak–Ribière–Polyak method under the exact line search and satisfies the sufficient descent condition independent of the line search and the objective function convexity. Similar to the Polak–Ribière–Polyak method, the method possesses an automatic restart feature which avoids jamming. Global convergence analyses are conducted when the line search fulfills the popular Wolfe conditions as well as an Armijo-type condition. Numerical experiments are done on a set of CUTEr unconstrained optimization test problems. Results of comparisons show computational efficiency of the proposed method in the sense of Dolan–Moré performance profile.
Accepté le :
DOI : 10.1051/ro/2016009
Mots-clés : Unconstrained optimization, conjugate gradient method, sufficient descent condition, line search, global convergence
@article{RO_2016__50_3_567_0,
author = {Babaie-Kafaki, Saman and Ghanbari, Reza},
title = {A descent hybrid modification of the {Polak{\textendash}Ribi\`ere{\textendash}Polyak} conjugate gradient method},
journal = {RAIRO - Operations Research - Recherche Op\'erationnelle},
pages = {567--574},
publisher = {EDP-Sciences},
volume = {50},
number = {3},
year = {2016},
doi = {10.1051/ro/2016009},
mrnumber = {3538840},
zbl = {1354.90174},
language = {en},
url = {http://archive.numdam.org/articles/10.1051/ro/2016009/}
}
TY - JOUR AU - Babaie-Kafaki, Saman AU - Ghanbari, Reza TI - A descent hybrid modification of the Polak–Ribière–Polyak conjugate gradient method JO - RAIRO - Operations Research - Recherche Opérationnelle PY - 2016 SP - 567 EP - 574 VL - 50 IS - 3 PB - EDP-Sciences UR - http://archive.numdam.org/articles/10.1051/ro/2016009/ DO - 10.1051/ro/2016009 LA - en ID - RO_2016__50_3_567_0 ER -
%0 Journal Article %A Babaie-Kafaki, Saman %A Ghanbari, Reza %T A descent hybrid modification of the Polak–Ribière–Polyak conjugate gradient method %J RAIRO - Operations Research - Recherche Opérationnelle %D 2016 %P 567-574 %V 50 %N 3 %I EDP-Sciences %U http://archive.numdam.org/articles/10.1051/ro/2016009/ %R 10.1051/ro/2016009 %G en %F RO_2016__50_3_567_0
Babaie-Kafaki, Saman; Ghanbari, Reza. A descent hybrid modification of the Polak–Ribière–Polyak conjugate gradient method. RAIRO - Operations Research - Recherche Opérationnelle, Tome 50 (2016) no. 3, pp. 567-574. doi : 10.1051/ro/2016009. http://archive.numdam.org/articles/10.1051/ro/2016009/
, A modified Polak–Ribière–Polyak conjugate gradient algorithm for unconstrained optimization. Optimization 60 (2011) 1457–1471. | DOI | MR | Zbl
, An adaptive conjugate gradient algorithm for large–scale unconstrained optimization. J. Comput. Appl. Math. 292 (2016) 83–91. | DOI | MR | Zbl
, An eigenvalue study on the sufficient descent property of a modified Polak–Ribière–Polyak conjugate gradient method. Bull. Iranian Math. Soc. 40 (2014) 235–242. | MR | Zbl
and , A descent extension of the Polak–Ribière–Polyak conjugate gradient method. Comput. Math. Appl. 68 (2014) 2005–2011. | DOI | MR | Zbl
, A two-term PRP-based descent method. Numer. Funct. Anal. Optim. 28 (2007) 1217–1230. | DOI | MR | Zbl
and , New conjugacy conditions and related nonlinear conjugate gradient methods. Appl. Math. Optim. 43 (2001) 87–101. | DOI | MR | Zbl
, , , , and , Convergence properties of nonlinear conjugate gradient methods. SIAM J. Optim. 10 (1999) 348–358. | Zbl
, and , An improved spectral conjugate gradient algorithm for nonconvex unconstrained optimization problems. J. Optim. Theory Appl. 157 (2013) 820–842. | DOI | MR | Zbl
and , Benchmarking optimization software with performance profiles. Math. Program. 91 (2002) 201–213. | DOI | MR | Zbl
, and , New version of the three-term conjugate gradient method based on spectral scaling conjugacy condition that generates descent search direction. Appl. Math. Comput. 269 (2015) 606–617. | DOI | MR | Zbl
, and , A self-adjusting conjugate gradient method with sufficient descent condition and conjugacy condition. J. Optim. Theory Appl. 165 (2015) 225–241. | DOI | MR | Zbl
, , and , A modified Hestenes–Stiefel conjugate gradient method with sufficient descent condition and conjugacy condition. J. Comput. Appl. Math. 281 (2015) 239–249. | DOI | MR | Zbl
, and , CUTEr: a constrained and unconstrained testing environment, revisited. ACM Trans. Math. Softw. 29 (2003) 373–394. | DOI | Zbl
and , Algorithm 851: CG−Descent, a conjugate gradient method with guaranteed descent. ACM Trans. Math. Softw. 32 (2006) 113–137. | DOI | MR | Zbl
and , A survey of nonlinear conjugate gradient methods. Pac. J. Optim. 2 (2006) 35–58. | MR | Zbl
and , Methods of conjugate gradients for solving linear systems. J. Res. Nat. Bur. Standards 49 (1952) 409–436. | DOI | MR | Zbl
and , Note sur la convergence de méthodes de directions conjuguées. Rev. Française Informat. Recherche Opérationnelle 3 (1969) 35–43. | Numdam | MR | Zbl
, The conjugate gradient method in extreme problems. USSR Comp. Math. Math. Phys. 9 (1969) 94–112. | DOI | Zbl
W. Sun and Y.X. Yuan, Optimization Theory and Methods: Nonlinear Programming. Springer, New York (2006). | MR | Zbl
, and , New spectral PRP conjugate gradient method for unconstrained optimization. Appl. Math. Lett. 24 (2011) 16–22. | DOI | MR | Zbl
, and , Global convergence of modified Polak–Ribière–Polyak conjugate gradient methods with sufficient descent property. J. Ind. Manag. Optim. 4 (2008) 565–579. | DOI | MR | Zbl
, Modified nonlinear conjugate gradient methods with sufficient descent property for large-scale optimization problems. Optim. Lett. 3 (2009) 11–21. | DOI | MR | Zbl
, and , A descent modified Polak–Ribière–Polyak conjugate gradient method and its global convergence. IMA J. Numer. Anal. 26 (2006) 629–640. | DOI | MR | Zbl
Cité par Sources :
