On the Strong Convergence of a Sufficient Descent Polak-Ribière-Polyak Conjugate Gradient Method
Recently, Zhang et al. proposed a sufficient descent Polak-Ribière-Polyak (SDPRP) conjugate gradient method for large-scale unconstrained optimization problems and proved its global convergence in the sense that lim infk→∞∥∇f(xk)∥=0 when an Armijo-type line search is used. In this paper, motivated b...
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| Format: | Article |
| Language: | English |
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Wiley
2014-01-01
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| Series: | Abstract and Applied Analysis |
| Online Access: | http://dx.doi.org/10.1155/2014/283215 |
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| author | Min Sun Jing Liu |
| author_facet | Min Sun Jing Liu |
| author_sort | Min Sun |
| collection | DOAJ |
| description | Recently, Zhang et al. proposed a sufficient descent Polak-Ribière-Polyak (SDPRP) conjugate gradient method for large-scale unconstrained optimization problems and proved its global convergence in the sense that lim infk→∞∥∇f(xk)∥=0 when an Armijo-type line search is used. In this paper, motivated by the line searches proposed by Shi et al. and Zhang et al., we propose two new Armijo-type line searches and show that the SDPRP method has strong convergence in the sense that limk→∞∥∇f(xk)∥=0 under the two new line searches. Numerical results are reported to show the efficiency of the SDPRP with the new Armijo-type line searches in practical computation. |
| format | Article |
| id | doaj-art-3e401cf0106143648a00ec6524bc7de1 |
| institution | Kabale University |
| issn | 1085-3375 1687-0409 |
| language | English |
| publishDate | 2014-01-01 |
| publisher | Wiley |
| record_format | Article |
| series | Abstract and Applied Analysis |
| spelling | doaj-art-3e401cf0106143648a00ec6524bc7de12025-02-03T01:32:05ZengWileyAbstract and Applied Analysis1085-33751687-04092014-01-01201410.1155/2014/283215283215On the Strong Convergence of a Sufficient Descent Polak-Ribière-Polyak Conjugate Gradient MethodMin Sun0Jing Liu1School of Mathematics and Statistics, Zaozhuang University, Shandong 277160, ChinaSchool of Mathematics and Statistics, Zhejiang University of Finance and Economics, Hangzhou 310018, ChinaRecently, Zhang et al. proposed a sufficient descent Polak-Ribière-Polyak (SDPRP) conjugate gradient method for large-scale unconstrained optimization problems and proved its global convergence in the sense that lim infk→∞∥∇f(xk)∥=0 when an Armijo-type line search is used. In this paper, motivated by the line searches proposed by Shi et al. and Zhang et al., we propose two new Armijo-type line searches and show that the SDPRP method has strong convergence in the sense that limk→∞∥∇f(xk)∥=0 under the two new line searches. Numerical results are reported to show the efficiency of the SDPRP with the new Armijo-type line searches in practical computation.http://dx.doi.org/10.1155/2014/283215 |
| spellingShingle | Min Sun Jing Liu On the Strong Convergence of a Sufficient Descent Polak-Ribière-Polyak Conjugate Gradient Method Abstract and Applied Analysis |
| title | On the Strong Convergence of a Sufficient Descent Polak-Ribière-Polyak Conjugate Gradient Method |
| title_full | On the Strong Convergence of a Sufficient Descent Polak-Ribière-Polyak Conjugate Gradient Method |
| title_fullStr | On the Strong Convergence of a Sufficient Descent Polak-Ribière-Polyak Conjugate Gradient Method |
| title_full_unstemmed | On the Strong Convergence of a Sufficient Descent Polak-Ribière-Polyak Conjugate Gradient Method |
| title_short | On the Strong Convergence of a Sufficient Descent Polak-Ribière-Polyak Conjugate Gradient Method |
| title_sort | on the strong convergence of a sufficient descent polak ribiere polyak conjugate gradient method |
| url | http://dx.doi.org/10.1155/2014/283215 |
| work_keys_str_mv | AT minsun onthestrongconvergenceofasufficientdescentpolakribierepolyakconjugategradientmethod AT jingliu onthestrongconvergenceofasufficientdescentpolakribierepolyakconjugategradientmethod |