Subdifferential and optimality conditions for the difference of set-valued mappings
In this paper, an existence theorem of the subgradients for set-valued mappings, which introduced by Borwein (Math Scand 48:189-204, 1981), and relations between this subdifferential and the subdifferential introduced by Baier and Jahn (J Optim Theory Appl 100:233-240, 1999), are obtained. By using...
| Main Authors: | , , |
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| Format: | Journal Article |
| Published: |
2012
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| Online Access: | http://hdl.handle.net/20.500.11937/44285 |
| _version_ | 1848756956787900416 |
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| author | Guo, X. Li, S. Teo, Kok Lay |
| author_facet | Guo, X. Li, S. Teo, Kok Lay |
| author_sort | Guo, X. |
| building | Curtin Institutional Repository |
| collection | Online Access |
| description | In this paper, an existence theorem of the subgradients for set-valued mappings, which introduced by Borwein (Math Scand 48:189-204, 1981), and relations between this subdifferential and the subdifferential introduced by Baier and Jahn (J Optim Theory Appl 100:233-240, 1999), are obtained. By using the concept of this subdifferential, the sufficient optimality conditions for generalized D. C. multiobjective optimization problems are established. And the necessary optimality conditions, which are the generalizations of that in Gadhi (Positivity 9:687-703, 2005), are also established. Moreover, by using a special scalarization function, a real set-valued optimization problem is introduced and the equivalent relations between the solutions are proved for the real set-valued optimization problem and a generalized D. C. multiobjective optimization problem. |
| first_indexed | 2025-11-14T09:20:26Z |
| format | Journal Article |
| id | curtin-20.500.11937-44285 |
| institution | Curtin University Malaysia |
| institution_category | Local University |
| last_indexed | 2025-11-14T09:20:26Z |
| publishDate | 2012 |
| recordtype | eprints |
| repository_type | Digital Repository |
| spelling | curtin-20.500.11937-442852017-09-13T14:29:23Z Subdifferential and optimality conditions for the difference of set-valued mappings Guo, X. Li, S. Teo, Kok Lay In this paper, an existence theorem of the subgradients for set-valued mappings, which introduced by Borwein (Math Scand 48:189-204, 1981), and relations between this subdifferential and the subdifferential introduced by Baier and Jahn (J Optim Theory Appl 100:233-240, 1999), are obtained. By using the concept of this subdifferential, the sufficient optimality conditions for generalized D. C. multiobjective optimization problems are established. And the necessary optimality conditions, which are the generalizations of that in Gadhi (Positivity 9:687-703, 2005), are also established. Moreover, by using a special scalarization function, a real set-valued optimization problem is introduced and the equivalent relations between the solutions are proved for the real set-valued optimization problem and a generalized D. C. multiobjective optimization problem. 2012 Journal Article http://hdl.handle.net/20.500.11937/44285 10.1007/s11117-011-0128-6 restricted |
| spellingShingle | Guo, X. Li, S. Teo, Kok Lay Subdifferential and optimality conditions for the difference of set-valued mappings |
| title | Subdifferential and optimality conditions for the difference of set-valued mappings |
| title_full | Subdifferential and optimality conditions for the difference of set-valued mappings |
| title_fullStr | Subdifferential and optimality conditions for the difference of set-valued mappings |
| title_full_unstemmed | Subdifferential and optimality conditions for the difference of set-valued mappings |
| title_short | Subdifferential and optimality conditions for the difference of set-valued mappings |
| title_sort | subdifferential and optimality conditions for the difference of set-valued mappings |
| url | http://hdl.handle.net/20.500.11937/44285 |