Global algorithm for solving linear multiplicative programming problems

This article presents a rectangular branch-and-bound algorithm with standard bisection rule for solving linear multiplicative problem (LMP). In this algorithm, a novel linear relaxation technique is presented for deriving the linear relaxation programming of problem LMP, which has separable characteristics and can be used to acquire the upper bound of the optimal value to problem LMP. Thus, to obtain a global optimal solution for problem LMP, the main computational work of the algorithm involves the solutions of a sequence of linear programming problems. Moreover, the proof of its convergence property and the numerical result show the feasibility and efficiency of the presented algorithm.