A smoothing scheme for optimization problems with max-min constraints
In this paper, we apply a smoothing approach to a minimization problem with a max-min constraint (i.e., a min-max-min problem). More specifically, we first rewrite the min-max-min problem as an optimization problem with several min-constraints and then approximate each min-constraint function by a s...
| Main Authors: | , , |
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| Format: | Journal Article |
| Published: |
American Institute of Mathematical Sciences
2007
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| Online Access: | http://aimsciences.org/journals/pdfs.jsp?paperID=2259&mode=full http://hdl.handle.net/20.500.11937/38706 |
| _version_ | 1848755393086357504 |
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| author | Huang, X. Yang, X. Teo, Kok |
| author_facet | Huang, X. Yang, X. Teo, Kok |
| author_sort | Huang, X. |
| building | Curtin Institutional Repository |
| collection | Online Access |
| description | In this paper, we apply a smoothing approach to a minimization problem with a max-min constraint (i.e., a min-max-min problem). More specifically, we first rewrite the min-max-min problem as an optimization problem with several min-constraints and then approximate each min-constraint function by a smooth function. As a result, the original min-max-min optimization problem can be solved by solving a sequence of smooth optimization problems. We investigate the relationship between the global optimal value and optimal solutions of the original min-max-min optimization problem and that of the approximate smooth problem. Under some conditions, we show that the limit points of the first-order (second-order) stationary points of the smooth optimization problems are first-order (second-order) stationary points of the original min-max-min optimization problem. |
| first_indexed | 2025-11-14T08:55:35Z |
| format | Journal Article |
| id | curtin-20.500.11937-38706 |
| institution | Curtin University Malaysia |
| institution_category | Local University |
| last_indexed | 2025-11-14T08:55:35Z |
| publishDate | 2007 |
| publisher | American Institute of Mathematical Sciences |
| recordtype | eprints |
| repository_type | Digital Repository |
| spelling | curtin-20.500.11937-387062017-01-30T14:25:03Z A smoothing scheme for optimization problems with max-min constraints Huang, X. Yang, X. Teo, Kok In this paper, we apply a smoothing approach to a minimization problem with a max-min constraint (i.e., a min-max-min problem). More specifically, we first rewrite the min-max-min problem as an optimization problem with several min-constraints and then approximate each min-constraint function by a smooth function. As a result, the original min-max-min optimization problem can be solved by solving a sequence of smooth optimization problems. We investigate the relationship between the global optimal value and optimal solutions of the original min-max-min optimization problem and that of the approximate smooth problem. Under some conditions, we show that the limit points of the first-order (second-order) stationary points of the smooth optimization problems are first-order (second-order) stationary points of the original min-max-min optimization problem. 2007 Journal Article http://hdl.handle.net/20.500.11937/38706 http://aimsciences.org/journals/pdfs.jsp?paperID=2259&mode=full American Institute of Mathematical Sciences restricted |
| spellingShingle | Huang, X. Yang, X. Teo, Kok A smoothing scheme for optimization problems with max-min constraints |
| title | A smoothing scheme for optimization problems with max-min constraints |
| title_full | A smoothing scheme for optimization problems with max-min constraints |
| title_fullStr | A smoothing scheme for optimization problems with max-min constraints |
| title_full_unstemmed | A smoothing scheme for optimization problems with max-min constraints |
| title_short | A smoothing scheme for optimization problems with max-min constraints |
| title_sort | smoothing scheme for optimization problems with max-min constraints |
| url | http://aimsciences.org/journals/pdfs.jsp?paperID=2259&mode=full http://hdl.handle.net/20.500.11937/38706 |