A Simplicial Branch and Bound Duality-Bounds Algorithm to Linear Multiplicative Programming

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: Xue-Gang Zhou, Bing-Yuan Cao
Format: Article
Language:English
Published: Hindawi Limited 2013-01-01
Series:Journal of Applied Mathematics
Online Access:http://dx.doi.org/10.1155/2013/984168
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spelling doaj-8d1159d45d8a47adb8278f3ba4947e0a2020-11-24T20:55:11ZengHindawi LimitedJournal 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
collection DOAJ
language English
format Article
sources DOAJ
author Xue-Gang Zhou
Bing-Yuan Cao
spellingShingle Xue-Gang Zhou
Bing-Yuan Cao
A Simplicial Branch and Bound Duality-Bounds Algorithm to Linear Multiplicative Programming
Journal of Applied Mathematics
author_facet Xue-Gang Zhou
Bing-Yuan Cao
author_sort Xue-Gang Zhou
title 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_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_sort simplicial branch and bound duality-bounds algorithm to linear multiplicative programming
publisher Hindawi Limited
series Journal of Applied Mathematics
issn 1110-757X
1687-0042
publishDate 2013-01-01
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.
url http://dx.doi.org/10.1155/2013/984168
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AT bingyuancao asimplicialbranchandbounddualityboundsalgorithmtolinearmultiplicativeprogramming
AT xuegangzhou simplicialbranchandbounddualityboundsalgorithmtolinearmultiplicativeprogramming
AT bingyuancao simplicialbranchandbounddualityboundsalgorithmtolinearmultiplicativeprogramming
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