Characterizations of Asymptotic Cone of the Solution Set of a Composite Convex Optimization Problem
We characterize the asymptotic cone of the solution set of a convex composite optimization problem. We then apply the obtained results to study the necessary and sufficient conditions for the nonemptiness and compactness of the solution set of the problem. Our results generalize and improve some kno...
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| Format: | Article |
| Language: | English |
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Wiley
2012-01-01
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| Series: | Journal of Applied Mathematics |
| Online Access: | http://dx.doi.org/10.1155/2012/617485 |
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| _version_ | 1832563709460873216 |
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| author | Zhe Chen |
| author_facet | Zhe Chen |
| author_sort | Zhe Chen |
| collection | DOAJ |
| description | We characterize the asymptotic cone of the solution set of a convex composite optimization problem. We then apply the obtained results to study the necessary and sufficient conditions for the nonemptiness and compactness of the solution set of the problem. Our results generalize and improve some known results in literature. |
| format | Article |
| id | doaj-art-5d771c256fcd481a90ac6000733515bc |
| institution | Kabale University |
| issn | 1110-757X 1687-0042 |
| language | English |
| publishDate | 2012-01-01 |
| publisher | Wiley |
| record_format | Article |
| series | Journal of Applied Mathematics |
| spelling | doaj-art-5d771c256fcd481a90ac6000733515bc2025-02-03T01:12:49ZengWileyJournal of Applied Mathematics1110-757X1687-00422012-01-01201210.1155/2012/617485617485Characterizations of Asymptotic Cone of the Solution Set of a Composite Convex Optimization ProblemZhe Chen0Department of Mathematics, Chongqing Normal University, Chongqing 400047, ChinaWe characterize the asymptotic cone of the solution set of a convex composite optimization problem. We then apply the obtained results to study the necessary and sufficient conditions for the nonemptiness and compactness of the solution set of the problem. Our results generalize and improve some known results in literature.http://dx.doi.org/10.1155/2012/617485 |
| spellingShingle | Zhe Chen Characterizations of Asymptotic Cone of the Solution Set of a Composite Convex Optimization Problem Journal of Applied Mathematics |
| title | Characterizations of Asymptotic Cone of the Solution Set of a Composite Convex Optimization Problem |
| title_full | Characterizations of Asymptotic Cone of the Solution Set of a Composite Convex Optimization Problem |
| title_fullStr | Characterizations of Asymptotic Cone of the Solution Set of a Composite Convex Optimization Problem |
| title_full_unstemmed | Characterizations of Asymptotic Cone of the Solution Set of a Composite Convex Optimization Problem |
| title_short | Characterizations of Asymptotic Cone of the Solution Set of a Composite Convex Optimization Problem |
| title_sort | characterizations of asymptotic cone of the solution set of a composite convex optimization problem |
| url | http://dx.doi.org/10.1155/2012/617485 |
| work_keys_str_mv | AT zhechen characterizationsofasymptoticconeofthesolutionsetofacompositeconvexoptimizationproblem |