Robust Approximate Optimality Conditions for Uncertain Nonsmooth Optimization with Infinite Number of Constraints
This paper deals with robust quasi approximate optimal solutions for a nonsmooth semi-infinite optimization problems with uncertainty data. By virtue of the epigraphs of the conjugates of the constraint functions, we first introduce a robust type closed convex constraint qualification. Then, by usin...
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| Format: | Article |
| Language: | English |
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MDPI AG
2018-12-01
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| Series: | Mathematics |
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| Online Access: | http://www.mdpi.com/2227-7390/7/1/12 |
| _version_ | 1819095322134052864 |
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| author | Xiangkai Sun Hongyong Fu Jing Zeng |
| author_facet | Xiangkai Sun Hongyong Fu Jing Zeng |
| author_sort | Xiangkai Sun |
| collection | DOAJ |
| description | This paper deals with robust quasi approximate optimal solutions for a nonsmooth semi-infinite optimization problems with uncertainty data. By virtue of the epigraphs of the conjugates of the constraint functions, we first introduce a robust type closed convex constraint qualification. Then, by using the robust type closed convex constraint qualification and robust optimization technique, we obtain some necessary and sufficient optimality conditions for robust quasi approximate optimal solution and exact optimal solution of this nonsmooth uncertain semi-infinite optimization problem. Moreover, the obtained results in this paper are applied to a nonsmooth uncertain optimization problem with cone constraints. |
| first_indexed | 2024-12-21T23:41:27Z |
| format | Article |
| id | doaj.art-79bbbb322e1b4ef08130c0e3fa5d618d |
| institution | Directory Open Access Journal |
| issn | 2227-7390 |
| language | English |
| last_indexed | 2024-12-21T23:41:27Z |
| publishDate | 2018-12-01 |
| publisher | MDPI AG |
| record_format | Article |
| series | Mathematics |
| spelling | doaj.art-79bbbb322e1b4ef08130c0e3fa5d618d2022-12-21T18:46:13ZengMDPI AGMathematics2227-73902018-12-01711210.3390/math7010012math7010012Robust Approximate Optimality Conditions for Uncertain Nonsmooth Optimization with Infinite Number of ConstraintsXiangkai Sun0Hongyong Fu1Jing Zeng2Chongqing Key Laboratory of Social Economy and Applied Statistics, College of Mathematics and Statistics, Chongqing Technology and Business University, Chongqing 400067, ChinaChina Research Institute of Enterprise Governed by Law, Southwest University of Political Science and Law, 301 Baosheng Street, Chongqing 401120, ChinaChongqing Key Laboratory of Social Economy and Applied Statistics, College of Mathematics and Statistics, Chongqing Technology and Business University, Chongqing 400067, ChinaThis paper deals with robust quasi approximate optimal solutions for a nonsmooth semi-infinite optimization problems with uncertainty data. By virtue of the epigraphs of the conjugates of the constraint functions, we first introduce a robust type closed convex constraint qualification. Then, by using the robust type closed convex constraint qualification and robust optimization technique, we obtain some necessary and sufficient optimality conditions for robust quasi approximate optimal solution and exact optimal solution of this nonsmooth uncertain semi-infinite optimization problem. Moreover, the obtained results in this paper are applied to a nonsmooth uncertain optimization problem with cone constraints.http://www.mdpi.com/2227-7390/7/1/12approximate quasi-solutionsoptimality conditionsrobust nonsmooth semi-infinite optimization |
| spellingShingle | Xiangkai Sun Hongyong Fu Jing Zeng Robust Approximate Optimality Conditions for Uncertain Nonsmooth Optimization with Infinite Number of Constraints Mathematics approximate quasi-solutions optimality conditions robust nonsmooth semi-infinite optimization |
| title | Robust Approximate Optimality Conditions for Uncertain Nonsmooth Optimization with Infinite Number of Constraints |
| title_full | Robust Approximate Optimality Conditions for Uncertain Nonsmooth Optimization with Infinite Number of Constraints |
| title_fullStr | Robust Approximate Optimality Conditions for Uncertain Nonsmooth Optimization with Infinite Number of Constraints |
| title_full_unstemmed | Robust Approximate Optimality Conditions for Uncertain Nonsmooth Optimization with Infinite Number of Constraints |
| title_short | Robust Approximate Optimality Conditions for Uncertain Nonsmooth Optimization with Infinite Number of Constraints |
| title_sort | robust approximate optimality conditions for uncertain nonsmooth optimization with infinite number of constraints |
| topic | approximate quasi-solutions optimality conditions robust nonsmooth semi-infinite optimization |
| url | http://www.mdpi.com/2227-7390/7/1/12 |
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