A new exact penalty method for semi-infinite programming problems
In this paper, we consider a class of nonlinear semi-infinite optimization problems. These problems involve continuous inequality constraints that need to be satisfied at every point in an infinite index set, as well as conventional equality and inequality constraints. By introducing a novel penalty...
| Main Authors: | , , , , |
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| Format: | Journal Article |
| Published: |
Elsevier
2014
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| Online Access: | http://hdl.handle.net/20.500.11937/22707 |
| _version_ | 1848750945376141312 |
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| author | Lin, Qun Loxton, Ryan Teo, Kok Lay Wu, Yong Hong Yu, C. |
| author_facet | Lin, Qun Loxton, Ryan Teo, Kok Lay Wu, Yong Hong Yu, C. |
| author_sort | Lin, Qun |
| building | Curtin Institutional Repository |
| collection | Online Access |
| description | In this paper, we consider a class of nonlinear semi-infinite optimization problems. These problems involve continuous inequality constraints that need to be satisfied at every point in an infinite index set, as well as conventional equality and inequality constraints. By introducing a novel penalty function to penalize constraint violations, we form an approximate optimization problem in which the penalty function is minimized subject to only bound constraints. We then show that this penalty function is exact—that is, when the penalty parameter is sufficiently large, any local solution of the approximate problem can be used to generate a corresponding local solution of the original problem. On this basis, the original problem can be solved as a sequence of approximate nonlinear programming problems. We conclude the paper with some numerical results demonstrating the applicability of our approach to PID control and filter design. |
| first_indexed | 2025-11-14T07:44:53Z |
| format | Journal Article |
| id | curtin-20.500.11937-22707 |
| institution | Curtin University Malaysia |
| institution_category | Local University |
| last_indexed | 2025-11-14T07:44:53Z |
| publishDate | 2014 |
| publisher | Elsevier |
| recordtype | eprints |
| repository_type | Digital Repository |
| spelling | curtin-20.500.11937-227072019-02-19T04:26:54Z A new exact penalty method for semi-infinite programming problems Lin, Qun Loxton, Ryan Teo, Kok Lay Wu, Yong Hong Yu, C. Semi-infinite programming Constrained optimization Exact penalty function Nonlinear programming In this paper, we consider a class of nonlinear semi-infinite optimization problems. These problems involve continuous inequality constraints that need to be satisfied at every point in an infinite index set, as well as conventional equality and inequality constraints. By introducing a novel penalty function to penalize constraint violations, we form an approximate optimization problem in which the penalty function is minimized subject to only bound constraints. We then show that this penalty function is exact—that is, when the penalty parameter is sufficiently large, any local solution of the approximate problem can be used to generate a corresponding local solution of the original problem. On this basis, the original problem can be solved as a sequence of approximate nonlinear programming problems. We conclude the paper with some numerical results demonstrating the applicability of our approach to PID control and filter design. 2014 Journal Article http://hdl.handle.net/20.500.11937/22707 10.1016/j.cam.2013.11.010 Elsevier fulltext |
| spellingShingle | Semi-infinite programming Constrained optimization Exact penalty function Nonlinear programming Lin, Qun Loxton, Ryan Teo, Kok Lay Wu, Yong Hong Yu, C. A new exact penalty method for semi-infinite programming problems |
| title | A new exact penalty method for semi-infinite programming problems |
| title_full | A new exact penalty method for semi-infinite programming problems |
| title_fullStr | A new exact penalty method for semi-infinite programming problems |
| title_full_unstemmed | A new exact penalty method for semi-infinite programming problems |
| title_short | A new exact penalty method for semi-infinite programming problems |
| title_sort | new exact penalty method for semi-infinite programming problems |
| topic | Semi-infinite programming Constrained optimization Exact penalty function Nonlinear programming |
| url | http://hdl.handle.net/20.500.11937/22707 |