Journal of Applied Mathematics

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

Xue-Gang Zhou and Bing-Yuan Cao

Full-text: Open access

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.

Article information

Source
J. Appl. Math., Volume 2013 (2013), Article ID 984168, 10 pages.

Dates
First available in Project Euclid: 14 March 2014

Permanent link to this document
https://projecteuclid.org/euclid.jam/1394807935

Digital Object Identifier
doi:10.1155/2013/984168

Mathematical Reviews number (MathSciNet)
MR3039751

Zentralblatt MATH identifier
1266.90126

Citation

Zhou, Xue-Gang; Cao, Bing-Yuan. A Simplicial Branch and Bound Duality-Bounds Algorithm to Linear Multiplicative Programming. J. Appl. Math. 2013 (2013), Article ID 984168, 10 pages. doi:10.1155/2013/984168. https://projecteuclid.org/euclid.jam/1394807935


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