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.
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