Existence of Solutions for Nonconvex and Nonsmooth Vector Optimization Problems
<p>Abstract</p> <p>We consider the weakly efficient solution for a class of nonconvex and nonsmooth vector optimization problems in Banach spaces. We show the equivalence between the nonconvex and nonsmooth vector optimization problem and the vector variational-like inequality invo...
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| Format: | Article |
| Language: | English |
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SpringerOpen
2008-01-01
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| Series: | Journal of Inequalities and Applications |
| Online Access: | http://www.journalofinequalitiesandapplications.com/content/2008/678014 |
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doaj-58135360e5fe4ec8a1c7e5275d6e03d62020-11-24T21:27:20ZengSpringerOpenJournal of Inequalities and Applications1025-58341029-242X2008-01-0120081678014Existence of Solutions for Nonconvex and Nonsmooth Vector Optimization ProblemsKim JongKyuHuang Nan-JingLiu Zhi-Bin<p>Abstract</p> <p>We consider the weakly efficient solution for a class of nonconvex and nonsmooth vector optimization problems in Banach spaces. We show the equivalence between the nonconvex and nonsmooth vector optimization problem and the vector variational-like inequality involving set-valued mappings. We prove some existence results concerned with the weakly efficient solution for the nonconvex and nonsmooth vector optimization problems by using the equivalence and Fan-KKM theorem under some suitable conditions.</p>http://www.journalofinequalitiesandapplications.com/content/2008/678014 |
| collection |
DOAJ |
| language |
English |
| format |
Article |
| sources |
DOAJ |
| author |
Kim JongKyu Huang Nan-Jing Liu Zhi-Bin |
| spellingShingle |
Kim JongKyu Huang Nan-Jing Liu Zhi-Bin Existence of Solutions for Nonconvex and Nonsmooth Vector Optimization Problems Journal of Inequalities and Applications |
| author_facet |
Kim JongKyu Huang Nan-Jing Liu Zhi-Bin |
| author_sort |
Kim JongKyu |
| title |
Existence of Solutions for Nonconvex and Nonsmooth Vector Optimization Problems |
| title_short |
Existence of Solutions for Nonconvex and Nonsmooth Vector Optimization Problems |
| title_full |
Existence of Solutions for Nonconvex and Nonsmooth Vector Optimization Problems |
| title_fullStr |
Existence of Solutions for Nonconvex and Nonsmooth Vector Optimization Problems |
| title_full_unstemmed |
Existence of Solutions for Nonconvex and Nonsmooth Vector Optimization Problems |
| title_sort |
existence of solutions for nonconvex and nonsmooth vector optimization problems |
| publisher |
SpringerOpen |
| series |
Journal of Inequalities and Applications |
| issn |
1025-5834 1029-242X |
| publishDate |
2008-01-01 |
| description |
<p>Abstract</p> <p>We consider the weakly efficient solution for a class of nonconvex and nonsmooth vector optimization problems in Banach spaces. We show the equivalence between the nonconvex and nonsmooth vector optimization problem and the vector variational-like inequality involving set-valued mappings. We prove some existence results concerned with the weakly efficient solution for the nonconvex and nonsmooth vector optimization problems by using the equivalence and Fan-KKM theorem under some suitable conditions.</p> |
| url |
http://www.journalofinequalitiesandapplications.com/content/2008/678014 |
| work_keys_str_mv |
AT kimjongkyu existenceofsolutionsfornonconvexandnonsmoothvectoroptimizationproblems AT huangnanjing existenceofsolutionsfornonconvexandnonsmoothvectoroptimizationproblems AT liuzhibin existenceofsolutionsfornonconvexandnonsmoothvectoroptimizationproblems |
| _version_ |
1725975262942724096 |