This paper explains a region-division-linearization algorithm for solving a class of generalized linear multiplicative programs (GLMPs) with positive exponent. In this algorithm, the original nonconvex problem GLMP is transformed into a series of linear programming problems by dividing the outer space of the problem GLMP into finite polynomial rectangles. A new two-stage acceleration technique is put in place to improve the computational efficiency of the algorithm, which removes part of the region of the optimal solution without problems GLMP in outer space. In addition, the global convergence of the algorithm is discussed, and the computational complexity of the algorithm is investigated. It demonstrates that the algorithm is a complete polynomial time approximation scheme. Finally, the numerical results show that the algorithm is effective and feasible.

中文翻译：

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一类具有正指数的广义线性乘法程序的有效多项式时间算法

本文介绍了一种求解一类具有正指数的广义线性乘法程序（GLMP）的区域划分线性化算法。在该算法中，通过将问题GLMP的外部空间划分为有限多项式矩形，将原始的非凸问题GLMP转换为一系列线性规划问题。提出了一种新的两阶段加速技术以提高算法的计算效率，该算法去除了最优解的部分区域，而在外层空间中没有问题。此外，讨论了该算法的全局收敛性，并研究了该算法的计算复杂度。证明了该算法是一个完整的多项式时间逼近方案。最后，