Second-Order Multiplier Iteration Based on a Class of Nonlinear Lagrangians
Nonlinear Lagrangian algorithm plays an important role in solving constrained optimization problems. It is known that, under appropriate conditions, the sequence generated by the first-order multiplier iteration converges superlinearly. This paper aims at analyzing the second-order multiplier iterat...
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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/10.1155/2014/210284 |
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| _version_ | 1832556080643702784 |
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| author | Yong-Hong Ren |
| author_facet | Yong-Hong Ren |
| author_sort | Yong-Hong Ren |
| collection | DOAJ |
| description | Nonlinear Lagrangian algorithm plays an important role in solving constrained optimization problems. It is known that, under appropriate conditions, the sequence generated by the first-order multiplier iteration converges superlinearly. This paper aims at analyzing the second-order multiplier iteration based on a class of nonlinear Lagrangians for solving nonlinear programming problems with inequality constraints. It is suggested that the sequence generated by the second-order multiplier iteration converges superlinearly with order at least two if in addition the Hessians of functions involved in problem are Lipschitz continuous. |
| format | Article |
| id | doaj-art-a19fc5c17dbe4518830a3a5f23dcf3d1 |
| 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-a19fc5c17dbe4518830a3a5f23dcf3d12025-02-03T05:46:26ZengWileyAbstract and Applied Analysis1085-33751687-04092014-01-01201410.1155/2014/210284210284Second-Order Multiplier Iteration Based on a Class of Nonlinear LagrangiansYong-Hong Ren0School of Control Science and Engineering, Dalian University of Technology, Dalian 116024, ChinaNonlinear Lagrangian algorithm plays an important role in solving constrained optimization problems. It is known that, under appropriate conditions, the sequence generated by the first-order multiplier iteration converges superlinearly. This paper aims at analyzing the second-order multiplier iteration based on a class of nonlinear Lagrangians for solving nonlinear programming problems with inequality constraints. It is suggested that the sequence generated by the second-order multiplier iteration converges superlinearly with order at least two if in addition the Hessians of functions involved in problem are Lipschitz continuous.http://dx.doi.org/10.1155/2014/210284 |
| spellingShingle | Yong-Hong Ren Second-Order Multiplier Iteration Based on a Class of Nonlinear Lagrangians Abstract and Applied Analysis |
| title | Second-Order Multiplier Iteration Based on a Class of Nonlinear Lagrangians |
| title_full | Second-Order Multiplier Iteration Based on a Class of Nonlinear Lagrangians |
| title_fullStr | Second-Order Multiplier Iteration Based on a Class of Nonlinear Lagrangians |
| title_full_unstemmed | Second-Order Multiplier Iteration Based on a Class of Nonlinear Lagrangians |
| title_short | Second-Order Multiplier Iteration Based on a Class of Nonlinear Lagrangians |
| title_sort | second order multiplier iteration based on a class of nonlinear lagrangians |
| url | http://dx.doi.org/10.1155/2014/210284 |
| work_keys_str_mv | AT yonghongren secondordermultiplieriterationbasedonaclassofnonlinearlagrangians |