中文摘要：

本文对符号线性比式和问题（P）提出了一个全局优化算法，这类优化问题广泛应用于工程设计、非线性系统稳定性分析等实际问题中．通过利用问题（P）的等价问题（Q）和线性松弛技术，建立了问题（Q）的松弛线性规划（RLP），通过对（RLP）可行域的细分以及一系列（RLP）的求解过程，从理论上证明了算法收敛到问题（P）的全局最优解．最终数值实验表明提出的方法是可行的．

英文摘要：

In this paper a global optimization algorithm is proposed for a class of linear sum of ratios problem （P）, which can be generally applied to engineering designs and stability analysis of nonlinear systems, and so on. By utilizing the equivalent Problem（Q） of problem（P） and linear relaxation technique, a relaxation linear programming （RLP） problem about problem（P） is established, through the successive refinement of the linear relaxation of the feasible region of the objection function and the solutions of a series of relaxation linear programming（RLP） ,and from theory the proof which the proposed branch and bound algorithm is convergent to the g!obal minimum is gived. And finally the numerical experiments are given to illustrate the feasibility of the proposed algorithm.