An Adaptive Prediction-Correction Method for Solving Large-Scale Nonlinear Systems of Monotone Equations with Applications
Combining multivariate spectral gradient method with projection scheme, this paper presents an adaptive prediction-correction method for solving large-scale nonlinear systems of monotone equations. The proposed method possesses some favorable properties: (1) it is progressive step by step, that is,...
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| Main Authors: | , , , |
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| Format: | Article |
| Language: | English |
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Wiley
2013-01-01
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| Series: | Abstract and Applied Analysis |
| Online Access: | http://dx.doi.org/10.1155/2013/619123 |
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| _version_ | 1832562549991669760 |
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| author | Gaohang Yu Shanzhou Niu Jianhua Ma Yisheng Song |
| author_facet | Gaohang Yu Shanzhou Niu Jianhua Ma Yisheng Song |
| author_sort | Gaohang Yu |
| collection | DOAJ |
| description | Combining multivariate spectral gradient method with projection scheme, this paper presents an adaptive prediction-correction method for solving large-scale nonlinear systems of monotone equations. The proposed method possesses some favorable properties: (1) it is progressive step by step, that is, the distance between iterates and the solution set is decreasing monotonically; (2) global convergence result is independent of the merit function and its Lipschitz continuity; (3) it is a derivative-free method and could be applied for solving large-scale nonsmooth equations due to its lower storage requirement. Preliminary numerical results show that the proposed method is very effective. Some practical applications of the proposed method are demonstrated and tested on sparse signal reconstruction, compressed sensing, and image deconvolution problems. |
| format | Article |
| id | doaj-art-a3bb2764782342c98588c1a9862397b0 |
| institution | Kabale University |
| issn | 1085-3375 1687-0409 |
| language | English |
| publishDate | 2013-01-01 |
| publisher | Wiley |
| record_format | Article |
| series | Abstract and Applied Analysis |
| spelling | doaj-art-a3bb2764782342c98588c1a9862397b02025-02-03T01:22:21ZengWileyAbstract and Applied Analysis1085-33751687-04092013-01-01201310.1155/2013/619123619123An Adaptive Prediction-Correction Method for Solving Large-Scale Nonlinear Systems of Monotone Equations with ApplicationsGaohang Yu0Shanzhou Niu1Jianhua Ma2Yisheng Song3School of Mathematics and Computer Sciences, Gannan Normal University, Ganzhou 341000, ChinaSchool of Biomedical Engineering, Southern Medical University, Guangzhou 510515, ChinaSchool of Biomedical Engineering, Southern Medical University, Guangzhou 510515, ChinaDepartment of Applied Mathematics, The Hong Kong Polytechnic University, Hong KongCombining multivariate spectral gradient method with projection scheme, this paper presents an adaptive prediction-correction method for solving large-scale nonlinear systems of monotone equations. The proposed method possesses some favorable properties: (1) it is progressive step by step, that is, the distance between iterates and the solution set is decreasing monotonically; (2) global convergence result is independent of the merit function and its Lipschitz continuity; (3) it is a derivative-free method and could be applied for solving large-scale nonsmooth equations due to its lower storage requirement. Preliminary numerical results show that the proposed method is very effective. Some practical applications of the proposed method are demonstrated and tested on sparse signal reconstruction, compressed sensing, and image deconvolution problems.http://dx.doi.org/10.1155/2013/619123 |
| spellingShingle | Gaohang Yu Shanzhou Niu Jianhua Ma Yisheng Song An Adaptive Prediction-Correction Method for Solving Large-Scale Nonlinear Systems of Monotone Equations with Applications Abstract and Applied Analysis |
| title | An Adaptive Prediction-Correction Method for Solving Large-Scale Nonlinear Systems of Monotone Equations with Applications |
| title_full | An Adaptive Prediction-Correction Method for Solving Large-Scale Nonlinear Systems of Monotone Equations with Applications |
| title_fullStr | An Adaptive Prediction-Correction Method for Solving Large-Scale Nonlinear Systems of Monotone Equations with Applications |
| title_full_unstemmed | An Adaptive Prediction-Correction Method for Solving Large-Scale Nonlinear Systems of Monotone Equations with Applications |
| title_short | An Adaptive Prediction-Correction Method for Solving Large-Scale Nonlinear Systems of Monotone Equations with Applications |
| title_sort | adaptive prediction correction method for solving large scale nonlinear systems of monotone equations with applications |
| url | http://dx.doi.org/10.1155/2013/619123 |
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