Journal of Applied Mathematics
Volume 2013 (2013), Article ID 984168, 10 pages
http://dx.doi.org/10.1155/2013/984168
Research Article

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

Xue-Gang Zhou1 and Bing-Yuan Cao2

1Department of Applied Mathematics, Guangdong University of Finance, Guangzhou, Guangdong 510521, China
2School of Mathematics and Information Science, Key Laboratory of Mathematics and Interdisciplinary Sciences of Guangdong, Higher Education Institutes, Guangzhou University, Guangzhou, Guangdong 510006, China

Received 12 September 2012; Revised 26 January 2013; Accepted 17 February 2013

Academic Editor: Frank Werner

Copyright © 2013 Xue-Gang Zhou and Bing-Yuan Cao. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

Abstract

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 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.