An Approximate Quasi-Newton Bundle-Type Method for Nonsmooth Optimization
An implementable algorithm for solving a nonsmooth convex optimization problem is proposed by combining Moreau-Yosida regularization and bundle and quasi-Newton ideas. In contrast with quasi-Newton bundle methods of Mifflin et al. (1998), we only assume that the values of the objective function and...
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| Format: | Article |
| Language: | English |
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Wiley
2013-01-01
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| Series: | Abstract and Applied Analysis |
| Online Access: | http://dx.doi.org/10.1155/2013/697474 |
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| author | Jie Shen Li-Ping Pang Dan Li |
| author_facet | Jie Shen Li-Ping Pang Dan Li |
| author_sort | Jie Shen |
| collection | DOAJ |
| description | An implementable algorithm for solving a nonsmooth convex optimization problem is proposed by combining Moreau-Yosida regularization and bundle and quasi-Newton ideas. In contrast with quasi-Newton bundle methods of Mifflin et al. (1998), we only assume that the values of the objective function and its subgradients are evaluated approximately, which makes the method easier to implement. Under some reasonable assumptions, the proposed method is shown to have a Q-superlinear rate of
convergence. |
| format | Article |
| id | doaj-art-569059a6fa87403b91315dc16e5c12a2 |
| institution | Kabale University |
| issn | 1085-3375 1687-0409 |
| language | English |
| publishDate | 2013-01-01 |
| publisher | Wiley |
| record_format | Article |
| series | Abstract and Applied Analysis |
| spelling | doaj-art-569059a6fa87403b91315dc16e5c12a22025-02-03T01:03:45ZengWileyAbstract and Applied Analysis1085-33751687-04092013-01-01201310.1155/2013/697474697474An Approximate Quasi-Newton Bundle-Type Method for Nonsmooth OptimizationJie Shen0Li-Ping Pang1Dan Li2School of Mathematics, Liaoning Normal University, Dalian 116029, ChinaSchool of Mathematical Sciences, Dalian University of Technology, Dalian 116024, ChinaSchool of Mathematical Sciences, Dalian University of Technology, Dalian 116024, ChinaAn implementable algorithm for solving a nonsmooth convex optimization problem is proposed by combining Moreau-Yosida regularization and bundle and quasi-Newton ideas. In contrast with quasi-Newton bundle methods of Mifflin et al. (1998), we only assume that the values of the objective function and its subgradients are evaluated approximately, which makes the method easier to implement. Under some reasonable assumptions, the proposed method is shown to have a Q-superlinear rate of convergence.http://dx.doi.org/10.1155/2013/697474 |
| spellingShingle | Jie Shen Li-Ping Pang Dan Li An Approximate Quasi-Newton Bundle-Type Method for Nonsmooth Optimization Abstract and Applied Analysis |
| title | An Approximate Quasi-Newton Bundle-Type Method for Nonsmooth Optimization |
| title_full | An Approximate Quasi-Newton Bundle-Type Method for Nonsmooth Optimization |
| title_fullStr | An Approximate Quasi-Newton Bundle-Type Method for Nonsmooth Optimization |
| title_full_unstemmed | An Approximate Quasi-Newton Bundle-Type Method for Nonsmooth Optimization |
| title_short | An Approximate Quasi-Newton Bundle-Type Method for Nonsmooth Optimization |
| title_sort | approximate quasi newton bundle type method for nonsmooth optimization |
| url | http://dx.doi.org/10.1155/2013/697474 |
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