A Global Optimization Algorithm for Sum of Linear Ratios Problem
We equivalently transform the sum of linear ratios programming problem into bilinear programming problem, then by using the linear characteristics of convex envelope and concave envelope of double variables product function, linear relaxation programming of the bilinear programming problem is given,...
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| Format: | Article |
| Language: | English |
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Wiley
2013-01-01
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| Series: | Journal of Applied Mathematics |
| Online Access: | http://dx.doi.org/10.1155/2013/276245 |
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| _version_ | 1832565570149548032 |
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| author | Yuelin Gao Siqiao Jin |
| author_facet | Yuelin Gao Siqiao Jin |
| author_sort | Yuelin Gao |
| collection | DOAJ |
| description | We equivalently transform the sum of linear ratios programming problem into bilinear programming problem, then by using the linear characteristics of convex envelope and concave envelope of double variables product function, linear relaxation programming of the bilinear programming problem is given, which can determine the lower bound of the optimal value of original problem. Therefore, a branch and bound algorithm for solving sum of linear ratios programming problem is put forward, and the convergence of the algorithm is proved. Numerical experiments are reported to show the effectiveness of the proposed algorithm. |
| format | Article |
| id | doaj-art-30abc778a07d43a4837532109ff05561 |
| institution | Kabale University |
| issn | 1110-757X 1687-0042 |
| language | English |
| publishDate | 2013-01-01 |
| publisher | Wiley |
| record_format | Article |
| series | Journal of Applied Mathematics |
| spelling | doaj-art-30abc778a07d43a4837532109ff055612025-02-03T01:07:10ZengWileyJournal of Applied Mathematics1110-757X1687-00422013-01-01201310.1155/2013/276245276245A Global Optimization Algorithm for Sum of Linear Ratios ProblemYuelin Gao0Siqiao Jin1Institute of Information & System Science, Beifang University of Nationalities, Yinchuan 750021, ChinaInstitute of Information & System Science, Beifang University of Nationalities, Yinchuan 750021, ChinaWe equivalently transform the sum of linear ratios programming problem into bilinear programming problem, then by using the linear characteristics of convex envelope and concave envelope of double variables product function, linear relaxation programming of the bilinear programming problem is given, which can determine the lower bound of the optimal value of original problem. Therefore, a branch and bound algorithm for solving sum of linear ratios programming problem is put forward, and the convergence of the algorithm is proved. Numerical experiments are reported to show the effectiveness of the proposed algorithm.http://dx.doi.org/10.1155/2013/276245 |
| spellingShingle | Yuelin Gao Siqiao Jin A Global Optimization Algorithm for Sum of Linear Ratios Problem Journal of Applied Mathematics |
| title | A Global Optimization Algorithm for Sum of Linear Ratios Problem |
| title_full | A Global Optimization Algorithm for Sum of Linear Ratios Problem |
| title_fullStr | A Global Optimization Algorithm for Sum of Linear Ratios Problem |
| title_full_unstemmed | A Global Optimization Algorithm for Sum of Linear Ratios Problem |
| title_short | A Global Optimization Algorithm for Sum of Linear Ratios Problem |
| title_sort | global optimization algorithm for sum of linear ratios problem |
| url | http://dx.doi.org/10.1155/2013/276245 |
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