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

A simplicial branch and bound duality-bounds algorithm is presentedto globally solving the linear multiplicative programming (LMP). We firstly convert the problem(LMP) into an equivalent programming one by introducing p auxiliary variables. During thebranch and bound search, the required lower bounds are computed by solving ordinary linearprogramming problems derived by using a Lagrangian duality theory. The proposed algorithmproves that it is convergent to a global minimum through the solutions to a series of linearprogramming problems. Some examples are given to illustrate the feasibility of the presentalgorithm