An Augmented Lagrangian Algorithm for Solving Semiinfinite Programming
We present a smooth augmented Lagrangian algorithm for semiinfinite programming (SIP). For this algorithm, we establish a perturbation theorem under mild conditions. As a corollary of the perturbation theorem, we obtain the global convergence result, that is, any accumulation point of the sequence g...
Saved in:
| Main Authors: | , |
|---|---|
| Format: | Article |
| Language: | English |
| Published: |
Wiley
2012-01-01
|
| Series: | Journal of Applied Mathematics |
| Online Access: | http://dx.doi.org/10.1155/2012/145083 |
| Tags: |
Add Tag
No Tags, Be the first to tag this record!
|
| _version_ | 1832545457307385856 |
|---|---|
| author | Qian Liu Changyu Wang |
| author_facet | Qian Liu Changyu Wang |
| author_sort | Qian Liu |
| collection | DOAJ |
| description | We present a smooth augmented Lagrangian algorithm for semiinfinite programming (SIP). For this algorithm, we establish a perturbation theorem under mild conditions. As a corollary of the perturbation theorem, we obtain the global convergence result, that is, any accumulation point of the sequence generated by the algorithm is the solution of SIP. We get this global convergence result without any boundedness condition or coercive condition. Another corollary of the perturbation theorem shows that the perturbation function at zero point is lower semi-continuous if and only if the algorithm forces the sequence of objective function convergence to the optimal value of SIP. Finally, numerical results are given. |
| format | Article |
| id | doaj-art-984829d24f9a4d35a122e43e87540768 |
| institution | Kabale University |
| issn | 1110-757X 1687-0042 |
| language | English |
| publishDate | 2012-01-01 |
| publisher | Wiley |
| record_format | Article |
| series | Journal of Applied Mathematics |
| spelling | doaj-art-984829d24f9a4d35a122e43e875407682025-02-03T07:25:48ZengWileyJournal of Applied Mathematics1110-757X1687-00422012-01-01201210.1155/2012/145083145083An Augmented Lagrangian Algorithm for Solving Semiinfinite ProgrammingQian Liu0Changyu Wang1Department of Mathematics, Shandong Normal University, Jinan, ChinaInstitute for Operations Research, Qufu Normal University, Qufu, ChinaWe present a smooth augmented Lagrangian algorithm for semiinfinite programming (SIP). For this algorithm, we establish a perturbation theorem under mild conditions. As a corollary of the perturbation theorem, we obtain the global convergence result, that is, any accumulation point of the sequence generated by the algorithm is the solution of SIP. We get this global convergence result without any boundedness condition or coercive condition. Another corollary of the perturbation theorem shows that the perturbation function at zero point is lower semi-continuous if and only if the algorithm forces the sequence of objective function convergence to the optimal value of SIP. Finally, numerical results are given.http://dx.doi.org/10.1155/2012/145083 |
| spellingShingle | Qian Liu Changyu Wang An Augmented Lagrangian Algorithm for Solving Semiinfinite Programming Journal of Applied Mathematics |
| title | An Augmented Lagrangian Algorithm for Solving Semiinfinite
Programming |
| title_full | An Augmented Lagrangian Algorithm for Solving Semiinfinite
Programming |
| title_fullStr | An Augmented Lagrangian Algorithm for Solving Semiinfinite
Programming |
| title_full_unstemmed | An Augmented Lagrangian Algorithm for Solving Semiinfinite
Programming |
| title_short | An Augmented Lagrangian Algorithm for Solving Semiinfinite
Programming |
| title_sort | augmented lagrangian algorithm for solving semiinfinite programming |
| url | http://dx.doi.org/10.1155/2012/145083 |
| work_keys_str_mv | AT qianliu anaugmentedlagrangianalgorithmforsolvingsemiinfiniteprogramming AT changyuwang anaugmentedlagrangianalgorithmforsolvingsemiinfiniteprogramming AT qianliu augmentedlagrangianalgorithmforsolvingsemiinfiniteprogramming AT changyuwang augmentedlagrangianalgorithmforsolvingsemiinfiniteprogramming |