A novel branch‐and‐bound algorithm for solving linear multiplicative programming problems

Abstract

This article proposes a rectangular branch‐and‐bound algorithm for solving linear multiplication problems (LMP) globally. In order to obtain a reliable lower bound of the original problem, this article designs a novel linear relaxation programming problem (LRP) that has not been seen in the existing literature. Based on the basic framework of the rectangular branch and bound algorithm, this article proposes an algorithm that can obtain a global solution. According to the structure of linear relaxation programming, the article designs a region reduction technology to improve the efficiency of the algorithm. This article also provides convergence analysis to ensure the reliability of the algorithm. Finally, several numerical experiments are used to demonstrate the effectiveness and robustness of the algorithm.