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

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.