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.

中文翻译：

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求解线性乘法规划问题的全局算法

本文提出了一种具有标准二等分规则的矩形分支定界算法，用于解决线性乘法问题（LMP）。在该算法中，提出了一种新颖的线性松弛技术，用于推导问题LMP的线性松弛规划，该技术具有可分离的特征，可以用来获取问题LMP的最优值的上限。因此，为了获得问题LMP的全局最优解，该算法的主要计算工作涉及一系列线性规划问题的解。此外，通过证明其收敛性和数值结果，证明了所提算法的可行性和有效性。