A Novel Approach for Solving Semidefinite Programs
A novel linearizing alternating direction augmented Lagrangian approach is proposed for effectively solving semidefinite programs (SDP). For every iteration, by fixing the other variables, the proposed approach alternatively optimizes the dual variables and the dual slack variables; then the primal...
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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: | Journal of Applied Mathematics |
| Online Access: | http://dx.doi.org/10.1155/2014/613205 |
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| _version_ | 1850232688668049408 |
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| author | Hong-Wei Jiao Ya-Kui Huang Jing Chen |
| author_facet | Hong-Wei Jiao Ya-Kui Huang Jing Chen |
| author_sort | Hong-Wei Jiao |
| collection | DOAJ |
| description | A novel linearizing alternating direction augmented Lagrangian approach is proposed for effectively solving semidefinite programs (SDP). For every iteration, by fixing the other variables, the proposed approach alternatively optimizes the dual variables and the dual slack variables; then the primal variables, that is, Lagrange multipliers, are updated. In addition, the proposed approach renews all the variables in closed forms without solving any system of linear equations. Global convergence of the proposed approach is proved under mild conditions, and two numerical problems are given to demonstrate the effectiveness of the presented approach. |
| format | Article |
| id | doaj-art-043e75ce87294d5f9a3836300d936ccf |
| institution | OA Journals |
| issn | 1110-757X 1687-0042 |
| language | English |
| publishDate | 2014-01-01 |
| publisher | Wiley |
| record_format | Article |
| series | Journal of Applied Mathematics |
| spelling | doaj-art-043e75ce87294d5f9a3836300d936ccf2025-08-20T02:03:06ZengWileyJournal of Applied Mathematics1110-757X1687-00422014-01-01201410.1155/2014/613205613205A Novel Approach for Solving Semidefinite ProgramsHong-Wei Jiao0Ya-Kui Huang1Jing Chen2Department of Mathematics, Henan Institute of Science and Technology, Xinxiang 453003, ChinaSchool of Mathematics and Statistics, Xidian University, Xi’an 710071, ChinaDepartment of Basic Science, Henan Mechanical and Electrical Engineering College, Xinxiang 453002, ChinaA novel linearizing alternating direction augmented Lagrangian approach is proposed for effectively solving semidefinite programs (SDP). For every iteration, by fixing the other variables, the proposed approach alternatively optimizes the dual variables and the dual slack variables; then the primal variables, that is, Lagrange multipliers, are updated. In addition, the proposed approach renews all the variables in closed forms without solving any system of linear equations. Global convergence of the proposed approach is proved under mild conditions, and two numerical problems are given to demonstrate the effectiveness of the presented approach.http://dx.doi.org/10.1155/2014/613205 |
| spellingShingle | Hong-Wei Jiao Ya-Kui Huang Jing Chen A Novel Approach for Solving Semidefinite Programs Journal of Applied Mathematics |
| title | A Novel Approach for Solving Semidefinite Programs |
| title_full | A Novel Approach for Solving Semidefinite Programs |
| title_fullStr | A Novel Approach for Solving Semidefinite Programs |
| title_full_unstemmed | A Novel Approach for Solving Semidefinite Programs |
| title_short | A Novel Approach for Solving Semidefinite Programs |
| title_sort | novel approach for solving semidefinite programs |
| url | http://dx.doi.org/10.1155/2014/613205 |
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