This paper aims to globally solve a generalized affine fractional program problem (GAFPP). Firstly, by introducing some outer space variables and performing equivalent transformations, we can derive the equivalence problem (EP) of the GAFPP. Secondly, by constructing a novel linear relaxation method, we can deduce the affine relaxation problem (ARP) of the EP. Next, by solving the ARP to compute the lower bound, we propose a new outer space branch-and-bound algorithm for tackling the GAFPP. Then, the global convergence of the algorithm is proved, and the computational complexity of the algorithm in the worst case is analyzed. Finally, numerical experimental results are reported to illustrate the effectiveness of the algorithm.

本文旨在全局解决广义仿射分数规划问题（GAFPP）。首先，通过引入一些外层空间变量并进行等价变换，我们可以推导出GAFPP的等价问题（EP）。其次，通过构造一种新的线性松弛方法，我们可以推导出EP的仿射松弛问题（ARP）。接下来，通过求解 ARP 来计算下界，我们提出了一种新的外层空间分支定界算法来解决 GAFPP。然后证明了算法的全局收敛性，并分析了最坏情况下算法的计算复杂度。最后，报告了数值实验结果以说明该算法的有效性。