A Rank-Two Feasible Direction Algorithm for the Binary Quadratic Programming
Based on the semidefinite programming relaxation of the binary quadratic programming, a rank-two feasible direction algorithm is presented. The proposed algorithm restricts the rank of matrix variable to be two in the semidefinite programming relaxation and yields a quadratic objective function with...
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| Main Authors: | , |
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| Format: | Article |
| Language: | English |
| Published: |
Wiley
2013-01-01
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| Series: | Journal of Applied Mathematics |
| Online Access: | http://dx.doi.org/10.1155/2013/963563 |
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| _version_ | 1850158255280488448 |
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| author | Xuewen Mu Yaling Zhang |
| author_facet | Xuewen Mu Yaling Zhang |
| author_sort | Xuewen Mu |
| collection | DOAJ |
| description | Based on the semidefinite programming relaxation of the binary quadratic programming, a rank-two feasible direction algorithm is presented. The proposed algorithm restricts the rank of matrix variable to be two in the semidefinite programming relaxation and yields a quadratic objective function with simple quadratic constraints. A feasible direction algorithm is used to solve the nonlinear programming. The convergent analysis and time complexity of the method is given.
Coupled with randomized algorithm, a suboptimal solution is obtained for the binary quadratic programming. At last, we report some numerical examples to compare our algorithm with randomized algorithm based on the interior point method and the feasible direction algorithm on max-cut problem. Simulation results have shown that our method is faster than the other two methods. |
| format | Article |
| id | doaj-art-69c4e44ad00f4ee2a73455d28fb2c06a |
| institution | OA Journals |
| issn | 1110-757X 1687-0042 |
| language | English |
| publishDate | 2013-01-01 |
| publisher | Wiley |
| record_format | Article |
| series | Journal of Applied Mathematics |
| spelling | doaj-art-69c4e44ad00f4ee2a73455d28fb2c06a2025-08-20T02:23:56ZengWileyJournal of Applied Mathematics1110-757X1687-00422013-01-01201310.1155/2013/963563963563A Rank-Two Feasible Direction Algorithm for the Binary Quadratic ProgrammingXuewen Mu0Yaling Zhang1School of Mathematics and Statistics, Xidian University, Xi’an 710071, ChinaSchool of Mathematics and Statistics, Xidian University, Xi’an 710071, ChinaBased on the semidefinite programming relaxation of the binary quadratic programming, a rank-two feasible direction algorithm is presented. The proposed algorithm restricts the rank of matrix variable to be two in the semidefinite programming relaxation and yields a quadratic objective function with simple quadratic constraints. A feasible direction algorithm is used to solve the nonlinear programming. The convergent analysis and time complexity of the method is given. Coupled with randomized algorithm, a suboptimal solution is obtained for the binary quadratic programming. At last, we report some numerical examples to compare our algorithm with randomized algorithm based on the interior point method and the feasible direction algorithm on max-cut problem. Simulation results have shown that our method is faster than the other two methods.http://dx.doi.org/10.1155/2013/963563 |
| spellingShingle | Xuewen Mu Yaling Zhang A Rank-Two Feasible Direction Algorithm for the Binary Quadratic Programming Journal of Applied Mathematics |
| title | A Rank-Two Feasible Direction Algorithm for the Binary Quadratic Programming |
| title_full | A Rank-Two Feasible Direction Algorithm for the Binary Quadratic Programming |
| title_fullStr | A Rank-Two Feasible Direction Algorithm for the Binary Quadratic Programming |
| title_full_unstemmed | A Rank-Two Feasible Direction Algorithm for the Binary Quadratic Programming |
| title_short | A Rank-Two Feasible Direction Algorithm for the Binary Quadratic Programming |
| title_sort | rank two feasible direction algorithm for the binary quadratic programming |
| url | http://dx.doi.org/10.1155/2013/963563 |
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