A Globally Convergent Matrix-Free Method for Constrained Equations and Its Linear Convergence Rate
A matrix-free method for constrained equations is proposed, which is a combination of the well-known PRP (Polak-Ribière-Polyak) conjugate gradient method and the famous hyperplane projection method. The new method is not only derivative-free, but also completely matrix-free, and consequently, it can...
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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/10.1155/2014/386030 |
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| author | Min Sun Jing Liu |
| author_facet | Min Sun Jing Liu |
| author_sort | Min Sun |
| collection | DOAJ |
| description | A matrix-free method for constrained equations is proposed, which is a combination of the well-known PRP (Polak-Ribière-Polyak) conjugate gradient method and the famous hyperplane projection method. The new method is not only derivative-free, but also completely matrix-free, and consequently, it can be applied to solve large-scale constrained equations. We obtain global convergence of the new method without any differentiability requirement on the constrained equations. Compared with the existing gradient methods for solving such problem, the new method possesses linear convergence rate under standard conditions, and a relax factor γ is attached in the update step to accelerate convergence. Preliminary numerical results show that it is promising in practice. |
| format | Article |
| id | doaj-art-269fd1d131244ba7a2f0e881f68e978e |
| 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-269fd1d131244ba7a2f0e881f68e978e2025-02-03T01:12:08ZengWileyAbstract and Applied Analysis1085-33751687-04092014-01-01201410.1155/2014/386030386030A Globally Convergent Matrix-Free Method for Constrained Equations and Its Linear Convergence RateMin Sun0Jing Liu1School of Mathematics and Statistics, Zaozhuang University, Shandong 277160, ChinaSchool of Mathematics and Statistics, Zhejiang University of Finance and Economics, Hangzhou 310018, ChinaA matrix-free method for constrained equations is proposed, which is a combination of the well-known PRP (Polak-Ribière-Polyak) conjugate gradient method and the famous hyperplane projection method. The new method is not only derivative-free, but also completely matrix-free, and consequently, it can be applied to solve large-scale constrained equations. We obtain global convergence of the new method without any differentiability requirement on the constrained equations. Compared with the existing gradient methods for solving such problem, the new method possesses linear convergence rate under standard conditions, and a relax factor γ is attached in the update step to accelerate convergence. Preliminary numerical results show that it is promising in practice.http://dx.doi.org/10.1155/2014/386030 |
| spellingShingle | Min Sun Jing Liu A Globally Convergent Matrix-Free Method for Constrained Equations and Its Linear Convergence Rate Abstract and Applied Analysis |
| title | A Globally Convergent Matrix-Free Method for Constrained Equations and Its Linear Convergence Rate |
| title_full | A Globally Convergent Matrix-Free Method for Constrained Equations and Its Linear Convergence Rate |
| title_fullStr | A Globally Convergent Matrix-Free Method for Constrained Equations and Its Linear Convergence Rate |
| title_full_unstemmed | A Globally Convergent Matrix-Free Method for Constrained Equations and Its Linear Convergence Rate |
| title_short | A Globally Convergent Matrix-Free Method for Constrained Equations and Its Linear Convergence Rate |
| title_sort | globally convergent matrix free method for constrained equations and its linear convergence rate |
| url | http://dx.doi.org/10.1155/2014/386030 |
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