Extension of Modified Polak-Ribière-Polyak Conjugate Gradient Method to Linear Equality Constraints Minimization Problems
Combining the Rosen gradient projection method with the two-term Polak-Ribière-Polyak (PRP) conjugate gradient method, we propose a two-term Polak-Ribière-Polyak (PRP) conjugate gradient projection method for solving linear equality constraints optimization problems. The proposed method possesses so...
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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/10.1155/2014/921364 |
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| _version_ | 1832552972177899520 |
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| author | Zhifeng Dai |
| author_facet | Zhifeng Dai |
| author_sort | Zhifeng Dai |
| collection | DOAJ |
| description | Combining the Rosen gradient projection method with the two-term Polak-Ribière-Polyak (PRP) conjugate gradient method, we propose a two-term Polak-Ribière-Polyak (PRP) conjugate gradient projection method for solving linear equality constraints optimization problems. The proposed method possesses some attractive properties: (1) search direction generated by the proposed method is a feasible descent direction; consequently the generated iterates are feasible points; (2) the sequences of function are decreasing. Under some mild conditions, we show that it is globally convergent with Armijio-type line search. Preliminary numerical results show that the proposed method is promising. |
| format | Article |
| id | doaj-art-3e893999deeb4fdf9be4fe012191b0a0 |
| 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-3e893999deeb4fdf9be4fe012191b0a02025-02-03T05:57:12ZengWileyAbstract and Applied Analysis1085-33751687-04092014-01-01201410.1155/2014/921364921364Extension of Modified Polak-Ribière-Polyak Conjugate Gradient Method to Linear Equality Constraints Minimization ProblemsZhifeng Dai0College of Business, Central South University, Hunan 410083, ChinaCombining the Rosen gradient projection method with the two-term Polak-Ribière-Polyak (PRP) conjugate gradient method, we propose a two-term Polak-Ribière-Polyak (PRP) conjugate gradient projection method for solving linear equality constraints optimization problems. The proposed method possesses some attractive properties: (1) search direction generated by the proposed method is a feasible descent direction; consequently the generated iterates are feasible points; (2) the sequences of function are decreasing. Under some mild conditions, we show that it is globally convergent with Armijio-type line search. Preliminary numerical results show that the proposed method is promising.http://dx.doi.org/10.1155/2014/921364 |
| spellingShingle | Zhifeng Dai Extension of Modified Polak-Ribière-Polyak Conjugate Gradient Method to Linear Equality Constraints Minimization Problems Abstract and Applied Analysis |
| title | Extension of Modified Polak-Ribière-Polyak Conjugate Gradient Method to Linear Equality Constraints Minimization Problems |
| title_full | Extension of Modified Polak-Ribière-Polyak Conjugate Gradient Method to Linear Equality Constraints Minimization Problems |
| title_fullStr | Extension of Modified Polak-Ribière-Polyak Conjugate Gradient Method to Linear Equality Constraints Minimization Problems |
| title_full_unstemmed | Extension of Modified Polak-Ribière-Polyak Conjugate Gradient Method to Linear Equality Constraints Minimization Problems |
| title_short | Extension of Modified Polak-Ribière-Polyak Conjugate Gradient Method to Linear Equality Constraints Minimization Problems |
| title_sort | extension of modified polak ribiere polyak conjugate gradient method to linear equality constraints minimization problems |
| url | http://dx.doi.org/10.1155/2014/921364 |
| work_keys_str_mv | AT zhifengdai extensionofmodifiedpolakribierepolyakconjugategradientmethodtolinearequalityconstraintsminimizationproblems |