The rate of convergence of the augmented Lagrangian method for nonlinear semidefinite programming
We analyze the rate of local convergence of the augmented Lagrangian method in nonlinear semidefinite optimization. The presence of the positive semidefinite cone constraint requires extensive tools such as the singular value decomposition of matrices, an implicit function theorem for semismooth fun...
| Main Authors: | , , |
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| Format: | Journal Article |
| Published: |
Springer
2008
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| Online Access: | http://hdl.handle.net/20.500.11937/18373 |
| _version_ | 1848749727219187712 |
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| author | Sun, D. Sun, Jie Zhang, L. |
| author_facet | Sun, D. Sun, Jie Zhang, L. |
| author_sort | Sun, D. |
| building | Curtin Institutional Repository |
| collection | Online Access |
| description | We analyze the rate of local convergence of the augmented Lagrangian method in nonlinear semidefinite optimization. The presence of the positive semidefinite cone constraint requires extensive tools such as the singular value decomposition of matrices, an implicit function theorem for semismooth functions, and variational analysis on the projection operator in the symmetric matrix space. Without requiring strict complementarity, we prove that, under the constraint nondegeneracy condition and the strong second order sufficient condition, the rate of convergence is linear and the ratio constant is proportional to 1/c, where c is the penalty parameter that exceeds a threshold c¯ > 0. |
| first_indexed | 2025-11-14T07:25:32Z |
| format | Journal Article |
| id | curtin-20.500.11937-18373 |
| institution | Curtin University Malaysia |
| institution_category | Local University |
| last_indexed | 2025-11-14T07:25:32Z |
| publishDate | 2008 |
| publisher | Springer |
| recordtype | eprints |
| repository_type | Digital Repository |
| spelling | curtin-20.500.11937-183732018-03-29T09:06:22Z The rate of convergence of the augmented Lagrangian method for nonlinear semidefinite programming Sun, D. Sun, Jie Zhang, L. We analyze the rate of local convergence of the augmented Lagrangian method in nonlinear semidefinite optimization. The presence of the positive semidefinite cone constraint requires extensive tools such as the singular value decomposition of matrices, an implicit function theorem for semismooth functions, and variational analysis on the projection operator in the symmetric matrix space. Without requiring strict complementarity, we prove that, under the constraint nondegeneracy condition and the strong second order sufficient condition, the rate of convergence is linear and the ratio constant is proportional to 1/c, where c is the penalty parameter that exceeds a threshold c¯ > 0. 2008 Journal Article http://hdl.handle.net/20.500.11937/18373 10.1007/s10107-007-0105-9 Springer restricted |
| spellingShingle | Sun, D. Sun, Jie Zhang, L. The rate of convergence of the augmented Lagrangian method for nonlinear semidefinite programming |
| title | The rate of convergence of the augmented Lagrangian method for nonlinear semidefinite programming |
| title_full | The rate of convergence of the augmented Lagrangian method for nonlinear semidefinite programming |
| title_fullStr | The rate of convergence of the augmented Lagrangian method for nonlinear semidefinite programming |
| title_full_unstemmed | The rate of convergence of the augmented Lagrangian method for nonlinear semidefinite programming |
| title_short | The rate of convergence of the augmented Lagrangian method for nonlinear semidefinite programming |
| title_sort | rate of convergence of the augmented lagrangian method for nonlinear semidefinite programming |
| url | http://hdl.handle.net/20.500.11937/18373 |