A Simplicial Branch and Bound Duality-Bounds Algorithm to Linear Multiplicative Programming
A simplicial branch and bound duality-bounds algorithm is presented to globally solving the linear multiplicative programming (LMP). We firstly convert the problem (LMP) into an equivalent programming one by introducing p auxiliary variables. During the branch and bound search, the required lower bo...
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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/10.1155/2013/984168 |
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| _version_ | 1849401501174202368 |
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| author | Xue-Gang Zhou Bing-Yuan Cao |
| author_facet | Xue-Gang Zhou Bing-Yuan Cao |
| author_sort | Xue-Gang Zhou |
| collection | DOAJ |
| description | A simplicial branch and bound duality-bounds algorithm is presented
to globally solving the linear multiplicative programming (LMP). We firstly convert the problem
(LMP) into an equivalent programming one by introducing p auxiliary variables. During the
branch and bound search, the required lower bounds are computed by solving ordinary linear
programming problems derived by using a Lagrangian duality theory. The proposed algorithm
proves that it is convergent to a global minimum through the solutions to a series of linear
programming problems. Some examples are given to illustrate the feasibility of the present
algorithm. |
| format | Article |
| id | doaj-art-8d1159d45d8a47adb8278f3ba4947e0a |
| 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-8d1159d45d8a47adb8278f3ba4947e0a2025-08-20T03:37:45ZengWileyJournal of Applied Mathematics1110-757X1687-00422013-01-01201310.1155/2013/984168984168A Simplicial Branch and Bound Duality-Bounds Algorithm to Linear Multiplicative ProgrammingXue-Gang Zhou0Bing-Yuan Cao1Department of Applied Mathematics, Guangdong University of Finance, Guangzhou, Guangdong 510521, ChinaSchool of Mathematics and Information Science, Key Laboratory of Mathematics and Interdisciplinary Sciences of Guangdong, Higher Education Institutes, Guangzhou University, Guangzhou, Guangdong 510006, ChinaA simplicial branch and bound duality-bounds algorithm is presented to globally solving the linear multiplicative programming (LMP). We firstly convert the problem (LMP) into an equivalent programming one by introducing p auxiliary variables. During the branch and bound search, the required lower bounds are computed by solving ordinary linear programming problems derived by using a Lagrangian duality theory. The proposed algorithm proves that it is convergent to a global minimum through the solutions to a series of linear programming problems. Some examples are given to illustrate the feasibility of the present algorithm.http://dx.doi.org/10.1155/2013/984168 |
| spellingShingle | Xue-Gang Zhou Bing-Yuan Cao A Simplicial Branch and Bound Duality-Bounds Algorithm to Linear Multiplicative Programming Journal of Applied Mathematics |
| title | A Simplicial Branch and Bound Duality-Bounds Algorithm to Linear Multiplicative Programming |
| title_full | A Simplicial Branch and Bound Duality-Bounds Algorithm to Linear Multiplicative Programming |
| title_fullStr | A Simplicial Branch and Bound Duality-Bounds Algorithm to Linear Multiplicative Programming |
| title_full_unstemmed | A Simplicial Branch and Bound Duality-Bounds Algorithm to Linear Multiplicative Programming |
| title_short | A Simplicial Branch and Bound Duality-Bounds Algorithm to Linear Multiplicative Programming |
| title_sort | simplicial branch and bound duality bounds algorithm to linear multiplicative programming |
| url | http://dx.doi.org/10.1155/2013/984168 |
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