A Simplicial Branch and Bound Duality-Bounds Algorithm to Linear Multiplicative Programming. (8th April 2013)

• Record Type: Journal Article
• Authors: Zhou, Xue-Gang; Cao, Bing-Yuan
• Other Names: Werner Frank Academic Editor.
• Is Part Of: Journal of applied mathematics. Volume 2013(2013)
• Publication Date: 2013-04-08
• Subjects: Mathematics -- Periodicals; 519.05
• DOI: 10.1155/2013/984168
• Languages: English
• ISSNs: 1110-757X

Abstract

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 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.