Second-order Karush-Kuhn-Tucker optimality conditions for set-valued optimization
In this paper, we propose the concept of a second-order composed contingent derivative for set-valued maps, discuss its relationship to the second-order contingent derivative and investigate some of its special properties. By virtue of the second-order composed contingent derivative, we extend the w...
| Main Authors: | , , |
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| Format: | Journal Article |
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Springer
2013
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| Online Access: | http://hdl.handle.net/20.500.11937/20256 |
| _version_ | 1848750255786426368 |
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| author | Zhu, S. Li, S. Teo, Kok Lay |
| author_facet | Zhu, S. Li, S. Teo, Kok Lay |
| author_sort | Zhu, S. |
| building | Curtin Institutional Repository |
| collection | Online Access |
| description | In this paper, we propose the concept of a second-order composed contingent derivative for set-valued maps, discuss its relationship to the second-order contingent derivative and investigate some of its special properties. By virtue of the second-order composed contingent derivative, we extend the well-known Lagrange multiplier rule and the Kurcyusz–Robinson–Zowe regularity assumption to a constrained set-valued optimization problem in the second-order case. Simultaneously, we also establish some second-order Karush–Kuhn–Tucker necessary and sufficient optimality conditions for a set-valued optimization problem, whose feasible set is determined by a set-valued map, under a generalized second-order Kurcyusz–Robinson–Zowe regularity assumption. |
| first_indexed | 2025-11-14T07:33:56Z |
| format | Journal Article |
| id | curtin-20.500.11937-20256 |
| institution | Curtin University Malaysia |
| institution_category | Local University |
| last_indexed | 2025-11-14T07:33:56Z |
| publishDate | 2013 |
| publisher | Springer |
| recordtype | eprints |
| repository_type | Digital Repository |
| spelling | curtin-20.500.11937-202562017-09-13T15:33:37Z Second-order Karush-Kuhn-Tucker optimality conditions for set-valued optimization Zhu, S. Li, S. Teo, Kok Lay optimality conditions Karush–Kuhn–Tucker condition second-order composed contingent derivative set-valued optimization regularity assumption lagrange multiplier rule In this paper, we propose the concept of a second-order composed contingent derivative for set-valued maps, discuss its relationship to the second-order contingent derivative and investigate some of its special properties. By virtue of the second-order composed contingent derivative, we extend the well-known Lagrange multiplier rule and the Kurcyusz–Robinson–Zowe regularity assumption to a constrained set-valued optimization problem in the second-order case. Simultaneously, we also establish some second-order Karush–Kuhn–Tucker necessary and sufficient optimality conditions for a set-valued optimization problem, whose feasible set is determined by a set-valued map, under a generalized second-order Kurcyusz–Robinson–Zowe regularity assumption. 2013 Journal Article http://hdl.handle.net/20.500.11937/20256 10.1007/s10898-013-0067-9 Springer restricted |
| spellingShingle | optimality conditions Karush–Kuhn–Tucker condition second-order composed contingent derivative set-valued optimization regularity assumption lagrange multiplier rule Zhu, S. Li, S. Teo, Kok Lay Second-order Karush-Kuhn-Tucker optimality conditions for set-valued optimization |
| title | Second-order Karush-Kuhn-Tucker optimality conditions for set-valued optimization |
| title_full | Second-order Karush-Kuhn-Tucker optimality conditions for set-valued optimization |
| title_fullStr | Second-order Karush-Kuhn-Tucker optimality conditions for set-valued optimization |
| title_full_unstemmed | Second-order Karush-Kuhn-Tucker optimality conditions for set-valued optimization |
| title_short | Second-order Karush-Kuhn-Tucker optimality conditions for set-valued optimization |
| title_sort | second-order karush-kuhn-tucker optimality conditions for set-valued optimization |
| topic | optimality conditions Karush–Kuhn–Tucker condition second-order composed contingent derivative set-valued optimization regularity assumption lagrange multiplier rule |
| url | http://hdl.handle.net/20.500.11937/20256 |