New Convergence Properties of the Primal Augmented Lagrangian Method
New convergence properties of the proximal augmented Lagrangian method is established for continuous nonconvex optimization problem with both equality and inequality constrains. In particular, the multiplier sequences are not required to be bounded. Different convergence results are discussed depend...
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| Main Authors: | , , , |
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| Format: | Article |
| Language: | English |
| Published: |
Wiley
2011-01-01
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| Series: | Abstract and Applied Analysis |
| Online Access: | http://dx.doi.org/10.1155/2011/902131 |
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| _version_ | 1832553608665628672 |
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| author | Jinchuan Zhou Xunzhi Zhu Lili Pan Wenling Zhao |
| author_facet | Jinchuan Zhou Xunzhi Zhu Lili Pan Wenling Zhao |
| author_sort | Jinchuan Zhou |
| collection | DOAJ |
| description | New convergence properties of the proximal augmented Lagrangian method is established for continuous nonconvex optimization problem with both equality and inequality constrains. In particular, the multiplier sequences are not required to be bounded. Different convergence results are discussed dependent on whether the iterative sequence {xk} generated by algorithm is convergent or divergent. Furthermore, under certain convexity assumption, we show that every accumulation point of {xk} is either a degenerate point or a KKT point of the primal problem. Numerical experiments are presented finally. |
| format | Article |
| id | doaj-art-6de75d3c7a314c60be56cb8ddf3dd64e |
| institution | Kabale University |
| issn | 1085-3375 1687-0409 |
| language | English |
| publishDate | 2011-01-01 |
| publisher | Wiley |
| record_format | Article |
| series | Abstract and Applied Analysis |
| spelling | doaj-art-6de75d3c7a314c60be56cb8ddf3dd64e2025-02-03T05:53:41ZengWileyAbstract and Applied Analysis1085-33751687-04092011-01-01201110.1155/2011/902131902131New Convergence Properties of the Primal Augmented Lagrangian MethodJinchuan Zhou0Xunzhi Zhu1Lili Pan2Wenling Zhao3Department of Mathematics, School of Science, Shandong University of Technology, Zibo 255049, ChinaDepartment of Mathematics, School of Science, Shandong University of Technology, Zibo 255049, ChinaDepartment of Mathematics, School of Science, Shandong University of Technology, Zibo 255049, ChinaDepartment of Mathematics, School of Science, Shandong University of Technology, Zibo 255049, ChinaNew convergence properties of the proximal augmented Lagrangian method is established for continuous nonconvex optimization problem with both equality and inequality constrains. In particular, the multiplier sequences are not required to be bounded. Different convergence results are discussed dependent on whether the iterative sequence {xk} generated by algorithm is convergent or divergent. Furthermore, under certain convexity assumption, we show that every accumulation point of {xk} is either a degenerate point or a KKT point of the primal problem. Numerical experiments are presented finally.http://dx.doi.org/10.1155/2011/902131 |
| spellingShingle | Jinchuan Zhou Xunzhi Zhu Lili Pan Wenling Zhao New Convergence Properties of the Primal Augmented Lagrangian Method Abstract and Applied Analysis |
| title | New Convergence Properties of the Primal Augmented Lagrangian Method |
| title_full | New Convergence Properties of the Primal Augmented Lagrangian Method |
| title_fullStr | New Convergence Properties of the Primal Augmented Lagrangian Method |
| title_full_unstemmed | New Convergence Properties of the Primal Augmented Lagrangian Method |
| title_short | New Convergence Properties of the Primal Augmented Lagrangian Method |
| title_sort | new convergence properties of the primal augmented lagrangian method |
| url | http://dx.doi.org/10.1155/2011/902131 |
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