A Note on Optimality Conditions for DC Programs Involving Composite Functions
By using the formula of the ε-subdifferential for the sum of a convex function with a composition of convex functions, some necessary and sufficient optimality conditions for a DC programming problem involving a composite function are obtained. As applications, a composed convex optimization problem...
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| Main Authors: | , |
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| Format: | Article |
| Language: | English |
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Wiley
2014-01-01
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| Series: | Abstract and Applied Analysis |
| Online Access: | http://dx.doi.org/10.1155/2014/203467 |
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| _version_ | 1849414448451682304 |
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| author | Xiang-Kai Sun Hong-Yong Fu |
| author_facet | Xiang-Kai Sun Hong-Yong Fu |
| author_sort | Xiang-Kai Sun |
| collection | DOAJ |
| description | By using the formula of the ε-subdifferential for the sum of a convex function with a composition of convex functions, some necessary and sufficient optimality conditions for a DC programming problem involving a composite function are obtained. As applications, a composed convex optimization problem, a DC optimization problem, and a convex optimization problem with a linear operator are examined at the end of this paper. |
| format | Article |
| id | doaj-art-67ba26301cf841c3b88ebbbd5767c072 |
| institution | Kabale University |
| issn | 1085-3375 1687-0409 |
| language | English |
| publishDate | 2014-01-01 |
| publisher | Wiley |
| record_format | Article |
| series | Abstract and Applied Analysis |
| spelling | doaj-art-67ba26301cf841c3b88ebbbd5767c0722025-08-20T03:33:50ZengWileyAbstract and Applied Analysis1085-33751687-04092014-01-01201410.1155/2014/203467203467A Note on Optimality Conditions for DC Programs Involving Composite FunctionsXiang-Kai Sun0Hong-Yong Fu1College of Mathematics and Statistics, Chongqing Technology and Business University, Chongqing 400067, ChinaSchool of Management, Southwest University of Political Science and Law, Chongqing 401120, ChinaBy using the formula of the ε-subdifferential for the sum of a convex function with a composition of convex functions, some necessary and sufficient optimality conditions for a DC programming problem involving a composite function are obtained. As applications, a composed convex optimization problem, a DC optimization problem, and a convex optimization problem with a linear operator are examined at the end of this paper.http://dx.doi.org/10.1155/2014/203467 |
| spellingShingle | Xiang-Kai Sun Hong-Yong Fu A Note on Optimality Conditions for DC Programs Involving Composite Functions Abstract and Applied Analysis |
| title | A Note on Optimality Conditions for DC Programs Involving Composite Functions |
| title_full | A Note on Optimality Conditions for DC Programs Involving Composite Functions |
| title_fullStr | A Note on Optimality Conditions for DC Programs Involving Composite Functions |
| title_full_unstemmed | A Note on Optimality Conditions for DC Programs Involving Composite Functions |
| title_short | A Note on Optimality Conditions for DC Programs Involving Composite Functions |
| title_sort | note on optimality conditions for dc programs involving composite functions |
| url | http://dx.doi.org/10.1155/2014/203467 |
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