An Approximate Proximal Bundle Method to Minimize a Class of Maximum Eigenvalue Functions
We present an approximate nonsmooth algorithm to solve a minimization problem, in which the objective function is the sum of a maximum eigenvalue function of matrices and a convex function. The essential idea to solve the optimization problem in this paper is similar to the thought of proximal bundl...
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| Main Authors: | , , , |
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| Format: | Article |
| Language: | English |
| Published: |
Wiley
2014-01-01
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| Series: | Journal of Applied Mathematics |
| Online Access: | http://dx.doi.org/10.1155/2014/893765 |
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| _version_ | 1832565485831454720 |
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| author | Wei Wang Lingling Zhang Miao Chen Sida Lin |
| author_facet | Wei Wang Lingling Zhang Miao Chen Sida Lin |
| author_sort | Wei Wang |
| collection | DOAJ |
| description | We present an approximate nonsmooth algorithm to solve a minimization problem, in which the objective function is the sum of a maximum eigenvalue function of matrices and a convex function. The essential idea to solve the optimization problem in this paper is similar to the thought of proximal bundle method, but the difference is that we choose approximate subgradient and function value to construct approximate cutting-plane model to solve the above mentioned problem. An important advantage of the approximate cutting-plane model for objective function is that it is more stable than cutting-plane model.
In addition, the approximate proximal bundle method algorithm can be given. Furthermore, the sequences generated by the algorithm converge to the optimal solution of the original problem. |
| format | Article |
| id | doaj-art-01b75dff5d62467c90417886795ba6fc |
| institution | Kabale University |
| issn | 1110-757X 1687-0042 |
| language | English |
| publishDate | 2014-01-01 |
| publisher | Wiley |
| record_format | Article |
| series | Journal of Applied Mathematics |
| spelling | doaj-art-01b75dff5d62467c90417886795ba6fc2025-02-03T01:07:25ZengWileyJournal of Applied Mathematics1110-757X1687-00422014-01-01201410.1155/2014/893765893765An Approximate Proximal Bundle Method to Minimize a Class of Maximum Eigenvalue FunctionsWei Wang0Lingling Zhang1Miao Chen2Sida Lin3School 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 Mathematical Sciences, Dalian University of Technology, Dalian 116024, ChinaWe present an approximate nonsmooth algorithm to solve a minimization problem, in which the objective function is the sum of a maximum eigenvalue function of matrices and a convex function. The essential idea to solve the optimization problem in this paper is similar to the thought of proximal bundle method, but the difference is that we choose approximate subgradient and function value to construct approximate cutting-plane model to solve the above mentioned problem. An important advantage of the approximate cutting-plane model for objective function is that it is more stable than cutting-plane model. In addition, the approximate proximal bundle method algorithm can be given. Furthermore, the sequences generated by the algorithm converge to the optimal solution of the original problem.http://dx.doi.org/10.1155/2014/893765 |
| spellingShingle | Wei Wang Lingling Zhang Miao Chen Sida Lin An Approximate Proximal Bundle Method to Minimize a Class of Maximum Eigenvalue Functions Journal of Applied Mathematics |
| title | An Approximate Proximal Bundle Method to Minimize a Class of Maximum Eigenvalue Functions |
| title_full | An Approximate Proximal Bundle Method to Minimize a Class of Maximum Eigenvalue Functions |
| title_fullStr | An Approximate Proximal Bundle Method to Minimize a Class of Maximum Eigenvalue Functions |
| title_full_unstemmed | An Approximate Proximal Bundle Method to Minimize a Class of Maximum Eigenvalue Functions |
| title_short | An Approximate Proximal Bundle Method to Minimize a Class of Maximum Eigenvalue Functions |
| title_sort | approximate proximal bundle method to minimize a class of maximum eigenvalue functions |
| url | http://dx.doi.org/10.1155/2014/893765 |
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