Geodesic
A descent hybrid modification of the Polak–Ribière–Polyak conjugate gradient method
Babaie-Kafaki, Saman1 ; Ghanbari, Reza2
1 Department of Mathematics, Faculty of Mathematics, Statistics and Computer Science, Semnan University, P.O. Box: 35195–363, Semnan, Iran.
2 Faculty of Mathematical Sciences, Ferdowsi University of Mashhad, P.O. Box: 9177948953, Mashhad, Iran.
RAIRO - Operations Research - Recherche Opérationnelle, Tome 50 (2016) no. 3, pp. 567-574

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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.

Reçu le :
Accepté le :
DOI : 10.1051/ro/2016009
Classification : 90C53, 49M37, 65K05
Keywords: Unconstrained optimization, conjugate gradient method, sufficient descent condition, line search, global convergence

Babaie-Kafaki, Saman 1 ; Ghanbari, Reza 2

1 Department of Mathematics, Faculty of Mathematics, Statistics and Computer Science, Semnan University, P.O. Box: 35195–363, Semnan, Iran.
2 Faculty of Mathematical Sciences, Ferdowsi University of Mashhad, P.O. Box: 9177948953, Mashhad, Iran. 
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     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},
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     year = {2016},
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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

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