A UV-Method for a Class of Constrained Minimized Problems of Maximum Eigenvalue Functions
In this paper, we apply the UV-algorithm to solve the constrained minimization problem of a maximum eigenvalue function which is the composite function of an affine matrix-valued mapping and its maximum eigenvalue. Here, we convert the constrained problem into its equivalent unconstrained problem by...
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| Main Authors: | , , , |
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| Format: | Article |
| Language: | English |
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Wiley
2017-01-01
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| Series: | Journal of Function Spaces |
| Online Access: | http://dx.doi.org/10.1155/2017/5309698 |
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| _version_ | 1832568260306927616 |
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| author | Wei Wang Ming Jin Shanghua Li Xinyu Cao |
| author_facet | Wei Wang Ming Jin Shanghua Li Xinyu Cao |
| author_sort | Wei Wang |
| collection | DOAJ |
| description | In this paper, we apply the UV-algorithm to solve the constrained minimization problem of a maximum eigenvalue function which is the composite function of an affine matrix-valued mapping and its maximum eigenvalue. Here, we convert the constrained problem into its equivalent unconstrained problem by the exact penalty function. However, the equivalent problem involves the sum of two nonsmooth functions, which makes it difficult to apply UV-algorithm to get the solution of the problem. Hence, our strategy first applies the smooth convex approximation of maximum eigenvalue function to get the approximate problem of the equivalent problem. Then the approximate problem, the space decomposition, and the U-Lagrangian of the object function at a given point will be addressed particularly. Finally, the UV-algorithm will be presented to get the approximate solution of the primal problem by solving the approximate problem. |
| format | Article |
| id | doaj-art-fec588ff39444433af5f463bd4b453fb |
| institution | Kabale University |
| issn | 2314-8896 2314-8888 |
| language | English |
| publishDate | 2017-01-01 |
| publisher | Wiley |
| record_format | Article |
| series | Journal of Function Spaces |
| spelling | doaj-art-fec588ff39444433af5f463bd4b453fb2025-02-03T00:59:28ZengWileyJournal of Function Spaces2314-88962314-88882017-01-01201710.1155/2017/53096985309698A UV-Method for a Class of Constrained Minimized Problems of Maximum Eigenvalue FunctionsWei Wang0Ming Jin1Shanghua Li2Xinyu Cao3School of Mathematics, Liaoning Normal University, Liaoning, Dalian 116029, ChinaSchool of Mathematics, Liaoning Normal University, Liaoning, Dalian 116029, ChinaSchool of Mathematics, Liaoning Normal University, Liaoning, Dalian 116029, ChinaSchool of Mathematics, Liaoning Normal University, Liaoning, Dalian 116029, ChinaIn this paper, we apply the UV-algorithm to solve the constrained minimization problem of a maximum eigenvalue function which is the composite function of an affine matrix-valued mapping and its maximum eigenvalue. Here, we convert the constrained problem into its equivalent unconstrained problem by the exact penalty function. However, the equivalent problem involves the sum of two nonsmooth functions, which makes it difficult to apply UV-algorithm to get the solution of the problem. Hence, our strategy first applies the smooth convex approximation of maximum eigenvalue function to get the approximate problem of the equivalent problem. Then the approximate problem, the space decomposition, and the U-Lagrangian of the object function at a given point will be addressed particularly. Finally, the UV-algorithm will be presented to get the approximate solution of the primal problem by solving the approximate problem.http://dx.doi.org/10.1155/2017/5309698 |
| spellingShingle | Wei Wang Ming Jin Shanghua Li Xinyu Cao A UV-Method for a Class of Constrained Minimized Problems of Maximum Eigenvalue Functions Journal of Function Spaces |
| title | A UV-Method for a Class of Constrained Minimized Problems of Maximum Eigenvalue Functions |
| title_full | A UV-Method for a Class of Constrained Minimized Problems of Maximum Eigenvalue Functions |
| title_fullStr | A UV-Method for a Class of Constrained Minimized Problems of Maximum Eigenvalue Functions |
| title_full_unstemmed | A UV-Method for a Class of Constrained Minimized Problems of Maximum Eigenvalue Functions |
| title_short | A UV-Method for a Class of Constrained Minimized Problems of Maximum Eigenvalue Functions |
| title_sort | uv method for a class of constrained minimized problems of maximum eigenvalue functions |
| url | http://dx.doi.org/10.1155/2017/5309698 |
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