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.
"A Simplicial Branch and Bound Duality-Bounds Algorithm to Linear Multiplicative Programming." J. Appl. Math. 2013 1 - 10, 2013. https://doi.org/10.1155/2013/984168