A Scaled Conjugate Gradient Method for Solving Monotone Nonlinear Equations with Convex Constraints
Based on the Scaled conjugate gradient (SCALCG) method presented by Andrei (2007) and the projection method presented by Solodov and Svaiter, we propose a SCALCG method for solving monotone nonlinear equations with convex constraints. SCALCG method can be regarded as a combination of conjugate gradi...
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| Format: | Article |
| Language: | English |
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Wiley
2013-01-01
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| Series: | Journal of Applied Mathematics |
| Online Access: | http://dx.doi.org/10.1155/2013/286486 |
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| _version_ | 1849467926468362240 |
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| author | Sheng Wang Hongbo Guan |
| author_facet | Sheng Wang Hongbo Guan |
| author_sort | Sheng Wang |
| collection | DOAJ |
| description | Based on the Scaled conjugate gradient (SCALCG) method presented by Andrei (2007) and the projection method presented by Solodov and Svaiter, we propose a SCALCG method for solving monotone nonlinear equations with convex constraints. SCALCG method can be regarded as a combination of conjugate gradient method and Newton-type method for solving unconstrained optimization problems. So, it has the advantages of the both methods. It is suitable for solving large-scale problems. So, it can be applied to solving large-scale monotone nonlinear equations with convex constraints. Under reasonable conditions, we prove its global convergence. We also do some numerical experiments show that the proposed method is efficient and promising. |
| format | Article |
| id | doaj-art-e132151be6854140a999d5c4d5495cbd |
| institution | Kabale University |
| issn | 1110-757X 1687-0042 |
| language | English |
| publishDate | 2013-01-01 |
| publisher | Wiley |
| record_format | Article |
| series | Journal of Applied Mathematics |
| spelling | doaj-art-e132151be6854140a999d5c4d5495cbd2025-08-20T03:25:59ZengWileyJournal of Applied Mathematics1110-757X1687-00422013-01-01201310.1155/2013/286486286486A Scaled Conjugate Gradient Method for Solving Monotone Nonlinear Equations with Convex ConstraintsSheng Wang0Hongbo Guan1Hunan Institute of Technology, Hengyang, Hunan 421008, ChinaHunan Institute of Technology, Hengyang, Hunan 421008, ChinaBased on the Scaled conjugate gradient (SCALCG) method presented by Andrei (2007) and the projection method presented by Solodov and Svaiter, we propose a SCALCG method for solving monotone nonlinear equations with convex constraints. SCALCG method can be regarded as a combination of conjugate gradient method and Newton-type method for solving unconstrained optimization problems. So, it has the advantages of the both methods. It is suitable for solving large-scale problems. So, it can be applied to solving large-scale monotone nonlinear equations with convex constraints. Under reasonable conditions, we prove its global convergence. We also do some numerical experiments show that the proposed method is efficient and promising.http://dx.doi.org/10.1155/2013/286486 |
| spellingShingle | Sheng Wang Hongbo Guan A Scaled Conjugate Gradient Method for Solving Monotone Nonlinear Equations with Convex Constraints Journal of Applied Mathematics |
| title | A Scaled Conjugate Gradient Method for Solving Monotone Nonlinear Equations with Convex Constraints |
| title_full | A Scaled Conjugate Gradient Method for Solving Monotone Nonlinear Equations with Convex Constraints |
| title_fullStr | A Scaled Conjugate Gradient Method for Solving Monotone Nonlinear Equations with Convex Constraints |
| title_full_unstemmed | A Scaled Conjugate Gradient Method for Solving Monotone Nonlinear Equations with Convex Constraints |
| title_short | A Scaled Conjugate Gradient Method for Solving Monotone Nonlinear Equations with Convex Constraints |
| title_sort | scaled conjugate gradient method for solving monotone nonlinear equations with convex constraints |
| url | http://dx.doi.org/10.1155/2013/286486 |
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