A novel global algorithm for solving linear multiplicative problem by integrating linear combination rule and branch-and-bound framework

This paper proposes a novel global algorithm to solve linear multiplicative problem (LMP) by integrating branch-and-bound framework with convex relaxation problem, linear combination rule and region reduction technique. Firstly, LMP is reformulated via D.C. form, and the reformulated LMP is converted into one of its equivalent problems. Secondly, a convex relaxation problem is constructed based on the characteristics of the equivalent problem and utilizing convex relaxation method. Thirdly, the linear combination rule and the region reduction technique are utilized to enhance efficiency of the algorithm and to reduce its computational time, respectively. Finally, numerical experiments validate that the new algorithm can solve LMP efficiently.